Question

ALGEBRA determine the angle measures in the polygon.a. 150°,135°,150°,135°b. 90°,135°,90°,90°,135°c. 30°, 135°,30°,30°,135°d. 90°,90°,90°,90°,90°

Answer 1

ANSWER

b. 90º, 135º, 90º, 90º, 135º

EXPLANATION

The sum of the measures of the interior angles of a polygon is:

$180º(n-2)$

Where n is the number of sides of the polygon. In this case n is 5. We know the measures of two angles and we know that the other three are congruent - because the three of them have xº. We can find x:

$\begin{gathered} 180(5-2)=135+135+x+x+x \\ 540=270+3x \end{gathered}$

Solving for x:

$\begin{gathered} 3x=540-270 \\ 3x=270 \\ x=\frac{270}{3} \\ x=90º \end{gathered}$

Therefore, the measures are 90º, 135º, 90º, 90º, 135º.