Question

In Fig. 6.39, sides QP and RQ of ∆ PQR are produced to points S and T respectively. If ∠ SPR = 135° and ∠ PQT = 110°, find ∠ PRQ?​

Answer 1

Answer:

may this answer help you and my writing is not so good

Answer 2

Answer:

• ★ ∠ PRQ = 65°

Step-by-step explanation:

★ Given :-

• ∠ SPR = 135°

• and ∠ PQT = 110°

★ To Find :-

• ∠ PRQ ?

★ Solution :-

Given ∠ SPR = 135 °

: $\implies$ ∠ PQT = 110° ∠ PRQ = ?

∠ SPR + ∠ RPQ = 180 ° ( by Linear pair )

: $\implies$ 135 ° + ∠ RPQ = 180 °

: $\implies$ ∠ RPQ = 180° - 135 °

: $\implies$ = 45

: $\implies$ ∠ PQT + ∠ PQR = 180 °

: $\implies$ ∠ PQR = 180 ° - 110 °

: $\implies$ = 70 °

In ∆ PQR

: $\implies$ ∠ P + ∠ Q + ∠ R = 180 °

: $\implies$ 45 ° + 70 ° + ∠ R = 180°

: $\implies$ 115 + ∠ R = 180 °

: $\implies$ ∠ R = 180° - 115 °

: $\implies$ = 65 °

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Additional information :

• The sum of all the internal angles of a triangle is always equal to  180 degrees.

• The sum of the length of any two sides of a triangle is always greater than the third side of the triangle.

• The difference between the length of any two sides of a triangle is always less than the length of the third side of the triangle.

• The side that is at the opposite side of the greater angle is always the longest side among all the three sides of a triangle.

• In a triangle the exterior angle is always equal to the sum of the interior opposite angle. this property is known as exterior angle property. 

• Any two triangles will be similar if their corresponding angles tend to be congruent and the length of their sides will be proportional.  

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