Question

the exterior angle PRS of triangle pqr is 105 degrees if Q is equal to 70 degree find Angle P is angle PRS less than angle p

Answer 1

Hey mate,, here is ur ans..

In triangle pqr,

∠PRS=105°

∠PQR=70°

we know that ,

exterior angle of a triangle is equal to sum 2 opposite angles in a triangle

⇒∠PRS = ∠PQR + ∠QPR

⇒105° = 70° + ∠QPR

⇒∠QPR = 35°

#hope it helps

 

Answer 2

Given: The exterior angle PRS of triangle pqr is 105 degrees if Q is equal to 70 degree.

To find: The angle P. Is angle PRS less than angle p.

Solution:

The line QRS is a straight line and hence, the angles QRP and PRS are supplementary. This means that the sum of these two angles is equal to 180°.

$QRP + PRS = 180$

$QRP + 105 = 180$

$QRP = 75$

Now, in the triangle PQR, ∠Q is 70°, ∠R is 75° and ∠P must be calculated. Since the sum of the measure of all the angles of a triangle must be 180°, the following equation can be written.

$\angle P + \angle Q + \angle R = 180$

$\angle P + 70 +75 = 180$

$\angle P = 35$

The angle PRS is 105° and the angle P is 35°. Thus, angle PRS is not less than angle P.

Therefore, the angle P is 35°. Angle PRS is not less than angle P.