Question

find the unknown angle a.​

Answer 1

Answer:

The sum of the exterior angle of all polygon is equal to 360deg.

let's name the exterior angles

a, b, c, d, e

a = a

b = x

c = 75

d = 77

e = 60

also

x + 131 = 180 ( linear pair )

x = 59

so

a + 59 + 75 + 77 + 60 = 360

a + 271 = 360

a = 360 - 271

a = 89

Answer 2

Hey!

• First of all I will find all the interior angles in the given Pentagon.

• Angle P = 180°-77° = 103°

• Angle Q = 180°-60° = 120°

• Angle T = 180°-75° = 105°

Now ;

Sum of the interior angles of Pentagon = 540°

• Angle P + Angle Q + Angle R + Angle S + Angle T = 540°

• 103° + 120° + Angle R + 131° + 105° = 540°

• 459° + Angle R = 540°

• Angle R (Interior) = 81°

Now ;

Angle R (Exterior) = 180°- 81° = 99°

Hope it helps!