Question

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Answer 1

Required Answer:-

GiveN:

A triangle PMN whose two of the exterior angles are x and y.

x > y

To Prove:

MP > NP

Step-by-step Explanation:

We have,

• x > y

Multiplying -1 both sides, and Remember! Whenever we multiply or divide an inequality by a negative number, you must flip the inequality sign.

➛ -x < -y

Now add 180° both sides,

➛ 180° - x < 180° - y

And in the figure, we can see that ∠PMN = 180° - x and ∠PNM = 180° - y. Hence,

➛ ∠PMN < ∠PNM

We know, The longest side in a triangle is opposite the largest angle, and the shortest side is opposite the smallest angle. ∠PMN is opposite to NP and ∠PNM is opposite to MP..

Thus:-

➛ PN < PM

Hence proved!!