Answer:
The value of y is 64 ⇒ first answer
Step-by-step 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
