SAT Math help » Geometry » plane Geometry » various other Polygons » just how to uncover an edge in a polygon

If edge A and angle C room complementary angles and also B and D space supplementary angles, i m sorry of the complying with must it is in true?


In isosceles triangle ABC, the measure of edge A is 50 degrees. I m sorry is no a feasible measure because that angle B?


65 degrees







Correct answer:

95 degrees


Explanation:

If edge 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 crest angle need to measure 80 degrees.

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If angle A is the crest angle, the 2 base angles have to be equal. Since 50 + x + x = 180 method x = 65, the 2 base angles have to measure 65 degrees.

The just number provided that is not feasible is 95 degrees.



Example question #3 : how To discover An angle In A Polygon


In triangle ABC, the measure of angle A = 70 degrees, the measure of angle Bx degrees, and the measure up of edge Cy degrees. What is the value of y in state of x?


70 + x







Correct answer:

110 – x


Explanation:

Since the three angles the a triangle amount to 180, we recognize that 70 + x + y = 180. Subtract 70 indigenous both sides and also see that x + y = 110. Subtract x native both sides and see the y = 110 – x.



Example concern #4 : just how To uncover An angle In A Polygon


What is the measure, in degrees, the each internal angle the a regular convex polygon that has actually twelve sides?


135







Correct answer:

150


Explanation:

The sum of the internal angles, in degrees, of a continuous polygon is given by the formula 180(n – 2), where n is the variety of sides. The problem pertains to a polygon with twelve sides, so we will certainly let n = 12. The sum of the inner angles in this polygon would certainly be 180(12 – 2) = 180(10) = 1800.

Because the polygon is constant (meaning the sides are all congruent), every one of the angles have actually the same measure. Thus, if we division the sum of the procedures of the angle by the number of sides, we will have actually the measure of each interior angle. In short, we should divide 1800 by 12, which gives us 150.

The prize is 150.



Example inquiry #5 : how To uncover An edge In A Polygon


*


Possible Answers:





Correct answer:

45


Explanation:

Angle FHI is the supplement of angle FHG, which is an interior angle in the octagon. Once two angles are supplementary, their sum is equal to 180 degrees. If us can uncover the measure up of each internal angle in the octagon, then we can discover the supplement of angle FHG, which will offer us the measure up of edge FHI.

The sum of the internal angles in a consistent polygon is provided by the formula 180(n – 2), wherein n is the number of sides in the polygon. An octagon has eight sides, for this reason the amount of the angles of the octagon is 180(8 – 2) = 180(6) = 1080 degrees. Since the octagon is regular, every one of its sides and angles room congruent. Thus, the measure up of each angle is equal to the amount of that is angles separated by 8. Therefore, each angle in the polygon has a measure of 1080/8 = 135 degrees. This method that angle FHG has actually a measure of 135 degrees.

Now that we know the measure of angle FHG, us can find the measure of FHI. The sum of the actions of FHG and FHI need to be 180 degrees, due to the fact that the two angles kind a line and also are supplementary. We deserve to write the following equation:

Measure the FHG + measure up of FHI = 180

135 + measure of FHI = 180

Subtract 135 native both sides.

See more: What Does Half Mean In Math, What Do Double And Half Mean

Measure of FHI = 45 degrees.

The prize is 45. 



Example question #6 : how To find An angle In A Polygon


What is the measure of each angle in a regular octagon?