Question

Find the measure of angle P and angle S if SP || RQ

Answer 1

Given: SP║RQ, ∠R = 90° and ∠Q = 130°.

To find: The measure of ∠P.

Answer:

It is given that SP║RQ. So let us assume that PQ is the transversal.

Therefore, ∠P + ∠Q = 180° (Co - interior Angles are Supplementary)

∠P + 130° = 180°

∠P = 180° - 130°

∠P = 50°

Now let us assume that SR is the transversal.

Therefore, ∠S + ∠R = 180° (Co - interior Angles are Supplementary)

∠S + 90° = 180°

∠S = 180° - 90°

∠S = 90°

Hope it helps :)

Answer 2

Answer:

Solution :

Let us assume , 5 + √3 is rational.

Let 5 + √3 = a/b , where a,b are

integers and b ≠ 0.

√3 = a/b - 5

=> √3 = ( a - 5b )/b

Since , a , b are integers , (a-5b)/b is

rational , and so √3 is rational . Find the measure of angle P and angle S if SP || RQ

This contradicts the fact that √3 is

irrational .

Hence , 5 + √3 is irrational.

Step-by-step explanation: