Question

question 1
3 pts
the measures of the exterior angles of a pentagon are 99°, 52°, 68°, 71°, and 2x°. what is the value of x?
360
70
35
36

Explanation:

Step1: Recall the sum of exterior angles of a polygon

The sum of the exterior angles of any polygon is \(360^{\circ}\).

Step2: Set up the equation

We know that \(99 + 52+68 + 71+2x=360\).
First, add the known angles: \(99 + 52+68 + 71=(99 + 71)+(52 + 68)=170+120 = 290\).
So the equation becomes \(290+2x = 360\).

Step3: Solve for \(x\)

Subtract \(290\) from both sides of the equation: \(2x=360 - 290\), so \(2x = 70\).
Divide both sides by \(2\): \(x=\frac{70}{2}=35\).

Answer:

35