Question

Which statement about the value of x is true?

Answer 1

180º = the sum of all angles in triangle
180º = 38 + 39 + PNO
180º = 77 + PNO
180º-77º= PNO
103º=PNO

PNM + PNO = 180 (straight line)
PNM + 103 = 180
PNM = 180-103
PNM = 77 = x

Answer 2

the value of x is 77

Explanation:

In triangle Δ PNO

∠OPN +∠PNO + ∠PON =180° (since, the sum of interior angles of triangle are 180)

38° +∠PNO + 39° = 180°

77° + ∠PNO = 180°

∠PNO = 180° - 77°

∠PNO = 103°

Since, MNO is straight line

then angle at N is ∠PNM + ∠PNO = 180°

In given figure ∠PNM is x°

∠PNM + ∠PNO = 180°

x° + 103° = 180°

x° = 180° -103°

x° = 77°

Hence, the value of x is 77