Question

In the given figure, PQ ⟂ QS and in

△PQR

∠P : ∠Q : ∠R = 9 : 7 : 2,

find the value of ∠SQT​

Answer 1

SOLUTION

GIVEN

In the given figure, PQ ⟂ QS and in△PQR

∠P : ∠Q : ∠R = 9 : 7 : 2

TO DETERMINE

The value of ∠SQT

EVALUATION

Here it is given that ∠P : ∠Q : ∠R = 9 : 7 : 2

Let ∠P = 9x , ∠Q = 7x , ∠R = 2x

We know that sum of three angles in a triangle is 180°

Thus we have

9x + 7x + 2x = 180°

⇒ 18x = 180°

⇒ x = 10°

So the three angles are

∠P = 90° , ∠Q = 70° , ∠R = 20°

Now it is given that PQ ⟂ QS

Thus we have ∠PQS = 90°

Again from the figure we see that

∠PQR + ∠PQS + ∠SQT = 180°

⇒ 70° + 90° + ∠SQT = 180°

⇒ 160° + ∠SQT = 180°

⇒ ∠SQT = 20°

FINAL ANSWER

∠SQT = 20°

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Answer 2

Answer:

SOLUTION

GIVEN

In the given figure, PQ ⟂ QS and in△PQR

∠P : ∠Q : ∠R = 9 : 7 : 2

TO DETERMINE

The value of ∠SQT

EVALUATION

Here it is given that ∠P : ∠Q : ∠R = 9 : 7 : 2

Let ∠P = 9x , ∠Q = 7x , ∠R = 2x

We know that sum of three angles in a triangle is 180°

Thus we have

9x + 7x + 2x = 180°

⇒ 18x = 180°

⇒ x = 10°

So the three angles are

∠P = 90° , ∠Q = 70° , ∠R = 20°

Now it is given that PQ ⟂ QS

Thus we have ∠PQS = 90°

Again from the figure we see that

∠PQR + ∠PQS + ∠SQT = 180°

⇒ 70° + 90° + ∠SQT = 180°

⇒ 160° + ∠SQT = 180°

⇒ ∠SQT = 20°

FINAL ANSWER

∠SQT = 20°