Properties of octagons, interior angles of octagons This image shows the process for a Using the same methods as for hexagons to the right (I'll let you do the pictures)... So, the sum of the interior angles of an octagon is 1080 degrees. To find the measure of the angles, we know that the sum of all the angles is 1080 degrees (from above)... And there are eight angles... So, the
measure of the interior angle of a regular octagon is 135 degrees. So, the measure of the central angle of a regular octagon is 45 degrees. All SAT Math ResourcesIf angle A and angle C are complementary angles and B and D are supplementary angles, which of the following must be true? Possible Answers: A * C > B * D AD = BC A/D < B/C None of the answers. Correct answer: None of the answers. Explanation: This question is very misleading, because while each answer COULD be true, none of them MUST be true. Between angle A and C, onne of the angles could be very small (0.001 degrees) and the other one could be very large. For instance, if A = 89.9999 and C = 0.0001, AC = 0.009. On the other hand, the two angles could be very siimilar. If B = 90 and D = 90 then BD = 8100 and BD > AC. If we use these same values we disprove AD = BC as 8100 ≠ .009. Finally, if B is a very small value, then B/C will be very small and smaller than A/D. In isosceles triangle ABC, the measure of angle A is 50 degrees. Which is NOT a possible measure for angle B? Possible Answers: 80 degrees There is more than one correct answer 65 degrees 50 degrees 95 degrees Correct answer: 95 degrees Explanation: If angle A is one of the base angles, then the other base angle must measure 50 degrees. Since 50 + 50 + x = 180 means x = 80, the vertex angle must measure 80 degrees. If angle A is the vertex angle, the two base angles must be equal. Since 50 + x + x = 180 means x = 65, the two base angles must measure 65 degrees. The only number given that is not possible is 95 degrees. In triangle ABC, the measure of angle A = 70 degrees, the measure of angle B = x degrees, and the measure of angle C = y degrees. What is the value of y in terms of x? Possible Answers: 110 – x 110 + x 70 – x 70 + x x – 70 Explanation: Since the three angles of a triangle sum to 180, we know that 70 + x + y = 180. Subtract 70 from both sides and see that x + y = 110. Subtract x from both sides and see that y = 110 – x. What is the measure, in degrees, of each interior angle of a regular convex polygon that has twelve sides? Explanation: The sum of the interior angles, in degrees, of a regular polygon is given by the formula 180(n – 2), where n is the number of sides. The problem concerns a polygon with twelve sides, so we will let n = 12. The sum of the interior angles in this polygon would be 180(12 – 2) = 180(10) = 1800. Because the polygon is regular (meaning its sides are all congruent), all of the angles have the same measure. Thus, if we divide the sum of the measures of the angles by the number of sides, we will have the measure of each interior angle. In short, we need to divide 1800 by 12, which gives us 150. The answer is 150. In the figure above, polygon ABDFHGEC is a regular octagon. What is the measure, in degrees, of angle FHI? Explanation: Angle FHI is the supplement of angle FHG, which is an interior angle in the octagon. When two angles are supplementary, their sum is equal to 180 degrees. If we can find the measure of each interior angle in the octagon, then we can find the supplement of angle FHG, which will give us the measure of angle FHI. The sum of the interior angles in a regular polygon is given by the formula 180(n – 2), where n is the number of sides in the polygon. An octagon has eight sides, so the sum of the angles of the octagon is 180(8 – 2) = 180(6) = 1080 degrees. Because the octagon is regular, all of its sides and angles are congruent. Thus, the measure of each angle is equal to the sum of its angles divided by 8. Therefore, each angle in the polygon has a measure of 1080/8 = 135 degrees. This means that angle FHG has a measure of 135 degrees. Now that we know the measure of angle FHG, we can find the measure of FHI. The sum of the measures of FHG and FHI must be 180 degrees, because the two angles form a line and are supplementary. We can write the following equation: Measure of FHG + measure of FHI = 180 135 + measure of FHI = 180 Subtract 135 from both sides. Measure of FHI = 45 degrees. The answer is 45. What is the measure of each angle in a regular octagon? Correct answer: Explanation: An octagon contains six triangles, or 1080 degrees. This means with 8 angles, each angle is 135 degrees. What is the measure of each central angle of an octagon? Correct answer: Explanation: There are 360 degrees and 8 angles, so dividing leaves 45 degrees per angle. What is the average (arithmetic mean) of all 15 interior angles of a quadrilateral, pentagon, and hexagon? Correct answer: Explanation: The 4 angles of a quadrilateral add to 360 The 5 angles of a pentagon add to 540 The 6 angles of a hexagon add to 720  Find the sum of the interior angles in a nonagon. Correct answer: Explanation: To solve, simply use the formula for the total degrees in a polygon, where n is the number of vertices. In this particular case, a nonagon is a shape with nine sides and thus nine vertices. Thus, Which of the following cannot be the measure of an exterior angle of a regular polygon? Correct answer: Explanation: If one exterior angle is taken at each vertex of any convex polygon, the sum of their measures is . In a regular polygon - one with congruent sides and congruent interior angles, each exterior angle is congruent to one another. If the polygon has sides, each exterior angle has measure . Given the common measure , Multiplying both sides by : and Since is equal to a number of sides, it is a whole number. Thus, we are looking for a value of which, when we divide 360 by it, yields a non-whole result. We see that is the correct choice, since'
A quick check confirms that 360 divided by 8, 10, 12, or 15 yields a whole result. All SAT Math ResourcesSAT Math Tutoring in Top Cities: Atlanta SAT Math Tutoring, Austin SAT Math Tutoring, Boston SAT Math Tutoring, Chicago SAT Math Tutoring, Dallas Fort Worth SAT Math Tutoring, Denver SAT Math Tutoring, Houston SAT Math Tutoring, Kansas City SAT Math Tutoring, Los Angeles SAT Math Tutoring, Miami SAT Math Tutoring, New York City SAT Math Tutoring, Philadelphia SAT Math Tutoring, Phoenix SAT Math Tutoring, San Diego SAT Math Tutoring, San Francisco-Bay Area SAT Math Tutoring, Seattle SAT Math Tutoring, St. Louis SAT Math Tutoring, Tucson SAT Math Tutoring, Washington DC SAT Math Tutoring SAT Math Tutors in Top Cities: Atlanta SAT Math Tutors, Austin SAT Math Tutors, Boston SAT Math Tutors, Chicago SAT Math Tutors, Dallas Fort Worth SAT Math Tutors, Denver SAT Math Tutors, Houston SAT Math Tutors, Kansas City SAT Math Tutors, Los Angeles SAT Math Tutors, Miami SAT Math Tutors, New York City SAT Math Tutors, Philadelphia SAT Math Tutors, Phoenix SAT Math Tutors, San Diego SAT Math Tutors, San Francisco-Bay Area SAT Math Tutors, Seattle SAT Math Tutors, St. Louis SAT Math Tutors, Tucson SAT Math Tutors, Washington DC SAT Math Tutors What is the measure of one of regular octagon?Each interior angle of a regular octagon =180∘−45∘=135∘
What is the measure of each side of a regular octagon?Regular Octagon
Eight congruent sides (sides of equal length) Eight congruent interior angles (each measuring 135°) Eight congruent exterior angles of 45°
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What is the measure of each angle of a regular octagon
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