What is m∠B?

There is a seven sided polygon ABCDEFG in which the measure of angle BCD is 148 degrees, the measure of angle DEF is 142 degrees, the measure of angle EFG is 130 degrees, the measure of angle FGA is 129 degrees, and the measure of angle GAB is 120 degrees. Angle CDE is a right angle.

A. 51°

B. 129°

C. 134°

D. 141°

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Yogeshkumariid Yogeshkumariid · Answer 1

The measure of angle B is 141 degrees

Given,

In the question:

There is a seven sided polygon ABCDEFG

The measure of angle BCD is 148 degrees,

The measure of angle DEF is 142 degrees,

The measure of angle EFG is 130 degrees,

The measure of angle FGA is 129 degrees,

and the measure of angle GAB is 120 degrees.

Angle CDE is a right angle.

To find the m∠B.

Now, According to the question:

The sum of angles in a polygon adds up to 180(n - 2), where n is the number of sides of the polygon

The angles are given as:

∠BCD = 148

∠DEF = 142

∠EFG = 130

∠FGA = 129

∠GAB = 120

∠CDE = 90

So, the measure of angle B is calculated using:

∠B + 148 + 142 + 130 + 129 + 120 + 90 = 180(n - 2)

∠B + 759 = 180(n - 2)

The value of n is 7

∠B + 759 = 180(7 - 2)

∠B + 759 = 180 x 5

∠B = 900 - 759

∠B = 141

Hence, the measure of angle B is 141 degrees

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