Question

help plizzzzzzzzzzzzzzzz,​

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!!

Answer 2

Solution:-

Given:

1. A triangle with exterior angles x and y.
2. ∠x > ∠y

To prove:

• MP > NP

Proof:

Given,

➡ ∠x > ∠y

Multiplying both sides by -1, We get,

➡ -∠x < -∠y

Adding 180° to both sides, We get,

➡ 180° - ∠x > 180° - ∠y

From figure,

180° - ∠x = ∠PMN and 180° - ∠y = ∠PNM

Therefore,

➡ ∠PMN < ∠PNM

We know that,

1. The longest side of a triangle is opposite to the longest angle and,
2. The shortest side of a triangle is opposite to the shortest angle.

Here, ∠PMN is opposite to NP.

Also, ∠PNM is opposite to MP.

So,

➡ NP < MP

➡ MP > NP (Hence Proved)