Question

Four of the interior angles of a Pentagon are congruent and the fifth angle is 3 times as large as the measure of the other four angles. what is the measure of each of the smaller angles? A 28b 33.75C 61D 99E 115Show work

Answer 1

Recall that there is a formula for the addition of all internal angles of a pentagon:

<1 + <2 +<3 + <4 + < 5 = 180 (5 - 2)

since four of the angles are congruent (let's consider for example <1 = <2 = <3 = <4 = x) we can write the equation above as:

4 x + <5 = 180 * 4 = 540

Now, consider as well that the fifth angle (<5) they tell us that it is 3 times as large as the measure of the other four angles.

1) If we interpret such statement as <5 = 3 * x

then we can solve the following equation:

4 x + 3 x = 540

7 x = 540

divide by 7 both sides:

x = 540 / 7

x = 77.14

2) if we interpret that <5 = 3 * 4x (three times the actual addition of the other 4 angles), then the equation becomes:

4 x + 12 x = 540

16 x = 540

x = 540 / 16

x = 33.75