Question

□PQRS is a cyclic quadrilateral. Side SR is extended to point T such that S-R-T then complete the following activity to prove
angel QRT = angel SPQ​

Answer 1

Answer:

it is a cyclic quadrilateral

angle SPQ+ angle SRQ=180

angle SRQ+angle QRT=180

angle SPQ+ angle SRQ= angle SRQ+ angle QRT

angle SPQ= angle QRT

Answer 2

Step-by-step explanation:

Given that,

PQRS is a cyclic quadrilateral.

We know,

The sum of two opposite angles in a cyclic quadrilateral is equal to 180° or we can say their sum is supplementary angles.

So,

• ∠SPQ + ∠SRQ = 180° -------- (i)

And, We also know that,

Sum of all angles forms on straight line are equal to 180° or Linear pair.

So,

• ∠SRQ + ∠QRT = 180°

(We need ∠QRT in prove, So we will find value of ∠SRQ in terms of ∠QRT)

⇒∠SRQ + ∠QRT = 180°

∠SRQ = 180° - ∠QRT ----------(ii)

Now, Take equation (i) :

⇒ ∠SPQ + ∠SRQ = 180°

• Put ∠SRQ = 180° - ∠QRT.

⇒ ∠SPQ + 180° - ∠QRT = 180° [By eq (ii)]

⇒ ∠SPQ - ∠QRT = 180° - 180°

⇒ ∠SPQ - ∠QRT = 0

⇒ ∠SPQ = ∠QRT

Hence, Proved!!