Question

please give me step by step solution it's really very important​

Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Given :-

In the above figure, the bisectors of ∠PQR and∠ PRS meet at O.

∠QTR = 40°

To find :-

Find ∠ QPR ?

Solution :-

From the given figure,

The bisectors of ∠PQR and ∠ PRS meet at O.

TQ is the bisector of ∠PQR

∠ PQR = ∠ PQY+ ∠ TQR

and∠ PQT = ∠ TQR

=> ∠ PQT = ∠ TQR = 1/2 ∠PQR --------(1)

and

PR is the bisector of ∠ PRS

∠ PRS = ∠PRT + ∠ TRS

and ∠PRT = ∠ TRS

∠PRT = ∠ TRS = 1/2 ∠ PRS -----------(2)

∠QTR = 40°

and

In ∆ PQR , ∠PRS is the exterior angle formed by the extending the side QR to S.

We know that

The exterior angle formed by the extending any side of a triangle is equal to the sum of the opposite interior angles .

∠PRS = ∠ QPR+ ∠PQR -----------(3)

and In another ∆ TQR, ∠TRS is the exterior angle

By using exterior angle property

∠TRS = ∠TQR +∠ QTR---------(4)

=> 1/2 ∠PRS = 1/2 ∠ PQR +∠ QTR

=> 1/2 ( ∠ QPR+∠PQR) = 1/2 ∠PQR+ ∠ QTR

=> 1/2 ∠QPR + 1/2 ∠PQR = 1/2 ∠ PQR + ∠QTR

=> 1/2 ∠ QPR = ∠QTR

=>∠QPR = 2× ∠ QTR

=> ∠QPR = 2×40°

=> ∠QPR = 80°

Therefore, ∠QPR = 80°

Answer:-

The measure of the angle ∠QPR is 80° for the given problem

Used formulae:-

Exterior angle property:-

• The exterior angle formed by the extending any side of a triangle is equal to the sum of the opposite interior angles .

• Amgle bisectors divides the angle into two equal parts.