∠mpr is an acute angle and pq is in the interior of ∠mpr. ∠qpr must be a. straight b. obtuse c. right d. acute

∠QPR must be an acute angle

Step-by-step 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.

D. Acute

Step-by-step 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: b.

step-by-step explanation:

the y coordinate for point b is 0, and answer b is the only one with that y coordinate.

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."