Question

In the figure QO and RO are bisectors of angle Q and angle R are respectively. if angle QPR is equal to 75 and angle PQR is equal to 56 then find the measure of angle ORQ.​

Answer 1

Answer:

This is actually easy!

$\bigstar GIVEN:$

• ∠QPR=75°
• ∠PQR=56°
• ∠PQO=∠OQR; ∠PRO=∠ORQ (OR and OQ are angle bisectors!!!)

$\bigstar SOLUTION:$

First, use angle sum property (QPR).

∠QPR+∠PQR+∠PRQ=180

75°+56°+∠PRQ=180°

∠PRQ=180°-131°

∠PRQ=49°.

We know that OQ bisects ∠PQR. Thus:

∠OQR=1/2×∠PQR

=1/2×56

=28°

Again, ∠ORQ=1/2×∠PRQ

=1/2×49

=24.5°

Done!!!

If you want to find ∠QOR use ASP:

24.5+28+∠QOR=180

∠QOR=180-52.5

∠QOR=127.5°

${\huge{\mathfrak{\underbrace{\blue{HOPE \:\: THIS \:\: HELPS \:\: :D}}}$

Answer 2

Given:

QO is the bisector of angle Q and RO is the bisector of angle Q.

Angle QPR= 75°, angle PQR= 56°.

To find:

The measure of angle ORQ.

Solution:

First of all, we need to find out the measure of angle PRQ.

From the angle sum property of a triangle, we have

In triangle PQR,

angle QPR + angle PQR + angle PRQ = 180°

75° + 56° + angle PRQ = 180°

angle PRQ = 180° - 131°

angle PRQ = 49°

As we know, the internal bisector of an angle divides the angle into equal halves. So, using the property of the internal angle bisector we have

angle PRO = angle ORQ (i)

Also,

angle PRQ = angle PRO + angle ORQ

angle PRQ= 2angle ORQ [from (i)]

angle ORQ= 49/2 (as angle PRQ = 49°)

angle ORQ= 24.5°.

Hence, the measure of angle ORQ is 24.5°.