For concave pentagon ABCDE, find the measure of the reflex angle at vertex E (in degrees) if m∠A = m∠D = x°, m∠B = m∠C = (4x)°, and the measure of the reflex angle at vertex E is (8x)°.

Step-by-step explanation:

First we need to calculate the sum of interior angle of the pentagon. The sum of interior angle of any polygon is expressed as S = (n-2)180

Given n = 5

S = (5-2)180

S = 3*180

S = 540°

Hence the measure of interior angle of the pentagon is 540°. The sum of all the interior angles will give us;

<A+<B+<C+<D+<E = 540

Given m∠A = m∠D = x°, m∠B = m∠C = (4x)° and the measure of reflex angle at E is (8x)°. If the reflex angle at E is (8x)°, the interior angle at E will be (360-8x)°

Substituting the given values into the formula to  get x;

x+4x+4x+x+360-8x = 540

10x-8x = 540-360

2x = 180

x = 180/2

x = 90°

To find the measure of the reflex angle at vertex E, we will substitute x = 90 into the vertex E = (8x)°.

vertex E  = 8(90)

vertex E  = 720°