Chapter 10: Inscribed Angles and Polygons

Question

 Find the measures of the interior angles of the polygon.

angle DAB = ___ degrees

angle ABC = ___ degrees

angle BCD = ___ degrees

angle ADC = ___ degrees

Answer 1

In geometry, always pay attention to what you have just learned. I'm sure there is a theorem that you just learned that opposite angles of a cyclic (inscribed) quadrilateral are supplementary.

Thus,

3x + 21y = 180

2x + 26y = 180

This is now an Algebra problem

Multiply the top equation by 2 and the bottom one by 3;

subtract the top equation from the bottom.

Solve for y, then x

6x + 42y = 360

6x + 78y = 540

36y = 180

y = 5

x = (180 - 21y)/3

x = (180 - 21(5))/3

x = (180 - 105)/3

x = 25

The angles, then, are

m ∠A = 26yº = 130°

m ∠B = 3xº = 75°

m ∠C = 2xº = 50°

m<D = 21yº = 105°

Note that 75+105 = 180

130+50 = 180