Question

∠MPR is an acute angle and PQ is in the interior of ∠MPR. ∠QPR must be

A. Straight
B. Obtuse
C. Right
D.Acute

Answer 1

Answer: D. Acute

Explanation:

We are given that : ∠MPR is an acute angle and PQ is in the interior of ∠MPR.

Definition :

Acute Angle : An angle having measure is less than 90°

.

Obtuse angle : An angle having measure is greater than 90° but less than 180

°.

Right angle : An angle whose measure exactly 90°

.

Straight angle : An angle whose measure exactly 180°

.

∵∠MPR is an acute angle ,

Then ∠MPR must be less than 90°

.

Also, PQ is in the interior of ∠MPR

.

⇒∠QPR should be less than ∠MPR

.

⇒ the measure of ∠QPR is also less than 90°

⇒∠QPR must be an acute angle . [By definition of Acute angle.]

Hence, the correct answer is option D.

Answer 2

∠QPR must be an acute angle

Explanation:

Given : ∠MPR is an acute angle and PQ is in the interior of ∠MPR.

To Find :∠QPR must be?

Solution:

Acute Angle : An angle whose measure is less than 90°

Since ∠MPR is an acute angle

This means ∠MPR is less than 90°

Now PQ is in the interior of ∠MPR

So, referring the attached figure

∠QPR should be less than ∠MPR

So, the measure of ∠QPR should be less than ∠MPR

So, the measure of ∠QPR is also less than 90°

So, ∠QPR must be an acute angle

So, Option D is correct.