Question

Find x.
find the measurement of angle b
find the measurment of angle c

Answer 1

x = 3, ∠ B = 70°, ∠ C = 50°

Explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ ADC is an exterior angle of the triangle , then

15x + 5 + 22x + 4 = 120 , that is

37x + 9 = 120 ( subtract 9 from both sides )

37x = 111 ( divide both sides by 37 )

x = 3

Thus

∠ B = 22x + 4 = 22(3) + 4 = 66 + 4 = 70°

∠ C = 15x + 5 = 15(3) + 5 = 45 + 5 = 50°

Answer 2

x = 3

Measurement of angle b: 70 degrees

Measurement of angle c: 70 degrees

Explanation:

120° = (15x + 5) + (22x + 4) (ext. ∠ of △)

120° = 15x + 22x + 5 + 4

(120 - 9)° = 37x

x = (111/37)

x = 3

Measurement of angle b: 22x = 4 = 22(3) + 4 = 66 + 4 = 70 degrees

Measurement of angle c: 15x + 5 = 15(3) + 5 = 45 + 5 = 50 degrees

Hope this helped!