Question

Consider the polygon shown. Determine the value of y. PLEASE HELP​

Answer 1

Answer:

y = 64°

Step-by-step explanation:

From the picture attached,

m(∠E) = 90°

m(∠E) = m(∠D)

m(∠B) + 67° = 180° [pair of linear angles]

m(∠B) = 113°

m(∠C) + 75° = 180°

m(∠C) = 180° - 75°

           = 105°

Since, sum of interior angles of a polygon = (n - 2) × 180°

Here, n = number of sides

For n = 5,

Sum of interior angles = (5 - 2) × 180°

                                     = 540°

m(∠A) + m(∠B) + m(∠C) + m(∠D) + m(∠E) = 540°

m(∠A) + 113° + 105° + m(∠D) + 90° = 540°

(m∠D) + m(∠D) = 540 - 308 [Since, m(∠A) = m(∠D)]

2(m∠D) = 232

m(∠D) = 116°

m(∠D) + y° = 180° [Linear pair of angles]

116 + y = 180

y = 64°