Answer:
The measure of angle B is 122° ⇒ answer D
Step-by-step 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°
