Question

Find the measure of angle B.

A. 186°

B. 12°

C. 128 4/7°

D. 122°

Answer 1

D

Explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 7, thus

sum = 180° × 5 = 900°

Sum the interior angles and equate to 900

12x - 9 + 9x + 14 + 133 +10x +9 + 10x + 136 +10x + 5 = 900, that is

51x + 288 = 900 ( subtract 288 from both sides )

51x = 612 ( divide both sides by 51 )

x = 12

Hence

∠B = 9x + 14 = (9 × 12) + 14 = 108 + 14 = 122° → D

Answer 2

The measure of angle B is 122° ⇒ answer D

Explanation:

* Lets explain how to solve the problem

- The sum of interior angles of any polygon can found by using this

rule (n - 2) × 180° , where n is the number of the sides or angles

of the polygon

∵ ABCDEFG is a polygon of 7 sides

∴ The sum of the measures of the interior angles = (7 - 2) × 180°

∴ The sum of the measures of the interior angles = 900°

∵ m∠A = 12x - 9 , m∠B = 9x + 14 , m∠C = 133° , m∠D = 10x + 9

∵ m∠E = 10x , m∠F = 136° , m∠G = 10x + 5

∵ The sum of all angles = 900°

∴ 12x - 9 + 9x + 14 + 133 + 10x + 9 + 10x + 136 + 10x + 5 = 900

∴ 51x + 288 = 900

- Subtract 288 from both sides

∴ 51x = 612

- Divide both sides by 51

∴ x = 12

∵ m∠B = 9x + 14

∵ x = 12

∴ m∠B = 9(12) + 14 = 122°

* The measure of angle B is 122°