Question

In the given figure, MNO is congruent to QPR by the SAS congruence condition. Find out the value of x.

Answer 1

Answer:

x = 10°

Step-by-step explanation:

Given:-

MNO ≅ QPR (By S.A.S Congruency)

∠RQP = 50°

∠PRQ = 70°

∠MNO = 5x + 10°

To Find:-

Value of x

Proof:-

We have,

MNO ≅ QPR

Then,

By C.P.C.T [Corresponding Parts of Congruent Triangles]

∠MNO = ∠QPR ---- 1

Now,

In ΔQPR,

∠RQP + ∠QPR + ∠PRQ = 180° [Angle Sum Property]

50° + ∠QPR + 70° = 180°

∠QPR + 120° = 180°

∠QPR = 180° - 120°

∠QPR = 60° ----- 2

From eq.1 and eq.2,

∠MNO = 60°

5x + 10° = 60°

5x = 60° - 10°

5x = 50°

x = 50°/5

x = 10°

Hence,

x = 10°

Hope it helped and believing you understood it........All the best