Answer:
m<A = 90°
m<B = 90°
m<C = 120°
m<D = 80°
m<E = 160°
Explanation:
Pre-Solving
We are given a pentagon, with the following angles: <A, <B, <C, <D, and <E.
<A and <B are right angles, and the measures of the other angles are 3x, 2x, and 4x respectively.
We want to find the measure of each angle.
Solving
As <A and <B are right angles, their angle measures are 90° each.
Recall that the sum of the interior angles in a pentagon is 540°. This means that m<A + m<B + m<C + m<D + m<E = 540°
We can substitute the values we know into the that equation.
90 + 90 + 3x + 2x + 4x = 540
Simplifying, we get:
180 + 9x = 540
Subtract 180 from both sides.
9x = 360
Divide both sides by 9.
x = 40
Now, substitute the value of x into 3x, 2x, and 4x to get the measures of the other angles.
m<C = 3x = 3(40) = 120°
m<D = 2x = 2(40) = 80°
m<E = 4x = 4(40) = 160°