Question

Find the values of x and y in the given figure.
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Answer 1

Answer:

x=45 (half of 90 degree)

Step-by-step explanation:

y=45+45+y=180 asm property

y=90

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Answer 2

Step-by-step explanation:

In the fig. ∆TQR,

$\sf\angle \: PTR = y$ [Given]

We know that,

The sum of the two opposite interior angles is equal to the exterior angle,

$\therefore\angle\: PTR = \angle\: TQR + \angle \: TRQ$

$\sf\Large\implies\: y = 30° + 45°$

$\sf\Large\implies\: \: \: {\boxed{y = 75°}}$

Again, in the fig. ∆TQS,

$\sf\angle\: TQS = 30° and \angle\: QTS = 50°$

By the se property taken above,

$\sf\angle\: TSR = \angle\: TQS + \angle\: QTS$

$\sf\Large\implies\: x = 30° + 50°$

$\sf\Large\implies\: \: \: {\boxed{x = 80°}}$

Hence, the value of x = 75° & y = 80°

$\pink{Hope \: it \: helps}$