Question

In ∆PRQ, side QR is extended to S. If ∠PRS = 150° and RP = RQ, find all the angles of ∆PRQ.​

Answer 1

Answer:

In the given triangle

applying : angle opposite to equal side are equal

so

angle RPQ= angle RQP= X. _______1

NOW,

since SRQ is a straight line so ,

angle SRP+ angle PRQ = 180

150 + angle PRQ=180

angle PRQ=30

now applying angle sum property of triangle

angle RPQ + angle RQP +angle PRQ= 180

x+ x+ 30 =180 (from 1)

2x+30=180

2x=150

x=75

so all the angles of ️ are

angle RPQ=75

angle RQP=75

angle PRQ=30

HOPE IT WILL HELP

Answer 2

• All angles of ∆PRQ are 35°, 75° and 75°.

Step-by-step explanation:

To find:-

• Measure of all angles of triangle.

Solution:-

If PR = QR

Then their opposite angles are also equal because if two sides of triangle are equal then their opposite angles are equal.

So,

$\leadsto$ ∠RPQ = x ---------(i)

We know,

Sum of all angles forms on straight line is equal to 180°. We also say this statement be linear pair.

So,

$\leadsto$ ∠PRQ + ∠PRS = 180°

$\leadsto$ ∠PRQ + 150° = 180°

$\leadsto$ ∠PRQ = 180° - 150°

$\leadsto$ ∠PRQ = 30°

We also know that,

Sum of all interior angles of triangle is 180°

So,

$\leadsto$ ∠PRQ + ∠RPQ + x = 180°

• By equation (i) ∠RPQ = x

$\leadsto$ 30° + x + x = 180°

$\leadsto$ 30° + 2x = 180°

$\leadsto$ 2x = 180° - 30°

$\leadsto$ 2x = 150°

$\leadsto$ x = 150°/2

$\leadsto$ x = 75°

∠PRQ, ∠RPQ and ∠PQR are angles of triangle:

∠PRQ = 30°

∠RPQ = ∠PQR = 75°

Therefore,

All angles of ∆PQR are 35°, 75° and 75°.