Question

Find the value of y (Angle A and angle B are congruent)

A) 64
B) 68
C) 71
D) 82

Answer 1

The correct answer is option A. 64

Explanation:

From the figure we can see a pentagon.

Sum of angles of a pentagon is 540

To find the value of m<B

From the figure we get, Angle A and angle B are congruent

m<A = m<B and one angle is 90°

Other two angles are,

180 - 75 = 105° and 180 - 67 = 113°

Also we can write,

105 + 113 + 90 + m<A + m<B = 540

308 + m<A + m<B = 540

m<A + m<B = 540 - 308 = 232

2m<B = 232

m<B = 232/2 = 116

To find the value of y

From figure we get,

<B + y = 180

y = 180 - <B

= 180 - 116 = 64

Therefore the correct answer is option A. 64

Answer 2

The value of y is 64 ⇒ first answer

Explanation:

* Lets study the figure to solve the question

- The figure is a polygon of 5 sides

- It has five interior angles and five exterior angles

- The sum of its interior angles depends on the number of its sides

- We can find the sum of the measures of its interior angles from this

rule ⇒ the sum = (n - 2) × 180°, where n is the number of its sides

- The sum of the measures of its exterior angles is 360°

(fixed for any polygon)

- The sum of the measure of an interior angle and its exterior angle

is 180°

∵ m∠A = m∠B

∴ The exterior angle of ∠A = the exterior angle of ∠B

∵ The exterior angle of ∠B is y°

∴ The exterior angle of ∠A is y°

∵ The measure of the interior angle of the exterior angle x° is 90°

∴ 90° + x° = 180° ⇒ subtract 90 from both sides

∴ x° = 90°

∵ The polygon has five exterior angles

# Angle of measure 75 , angle of measure 67 , y° , y° , x°

∴ 75° + 67° + y° + y° + x° = 360° ⇒ sum of the exterior angles

∵ x° = 90°

∴ 75° + 67° + y° + y° + 90° = 360° ⇒ simplify

∴ 232 + 2y° = 360° ⇒ subtract 232 from both sides

∴ 2y° = 128 ⇒ divide both sides by 2

∴ y° = 64°

* The value of y is 64