Question

Observe the figure given alongside and find the value of x.​

Answer 1

Solution -

See the attached figure .

Here , from this figure , we can gather the following information -

PQ = PM = MR .

So , we can say that -

∆ PQM is an isosceles triangle .

∆ PMR is an isosceles triangle.

So, ∠ MPR = ∠ MRP = x°

Now , using the exterior angle theorem , we can say -

∠ PMQ = ∠ MPR + ∠ MRP = 2x°

Now , ∠ PMQ = ∠ PQM = 2x°

Now ,

∠ PMQ + ∠ PQM + ∠ QPM = 180°

=> ∠ PMQ + ∠ PQM + 40° = 180°

=> ∠ PMQ + ∠ PQM = 140°

=> 2x + 2x = 140

=> 4x = 140

=> x = 35°

This is the answer .

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