Question

I know this answer is 65° but how explain​

Answer 1

Answer:

65° is the value of ∠PRQ.

Step-by-step explanation:

Given :-

∠SPR = 135°

∠PQT = 110°

Solution :-

In ∆PQR ,

∠RPQ = 180° - ∠RPS = 180° - 135° = 45°

∠PQR = 180° - ∠PQT = 180° - 110° = 70°

• a straight line is always 180°

∠PRQ = 180° - ( ∠RPQ + ∠PQR ) = 180°-( 45°+70°) = 180°-115° = 65°

Answer 2

Answer:

∠PRQ = 65°

Step-by-step explanation:

From the figure, we have:

=> ∠PQT = 110°

=> ∠SPR = 135°

We are asked to find:

=> ∠PRQ

Solution:

>> In the figure

=> TQR is a straight line

=> ∴ 110° + x° = 180°

=> x° = 70° [∠PQR]

>> In the figure

=> QPS is a straight line

=> ∴ 135° + x° = 180°

=> x° = 45° [∠RPQ]

Now, in ΔPQR,

=> ∠PQR + ∠RPQ + ∠PRQ = 180°

[ ∵ Angle sum property ]

=> 70° + 45° + ∠PRQ = 180°

=> 115° + ∠PRQ = 180°

=> ∠PRQ = 180° - 115°

=> ∠PRQ = 65°

Must know:

Angle sum property: Sum of all the interior angles in a triangle is equal to 180°

Straight line property: From the figure, we observe two straight lines QPS and TQR, when an angle lies on a straight line then the other angle and given angle's sum will be equal to 180°.