Question

find unknown angles in square PQRS​

Answer 1

Answer:

X=45°

Y=135°

Z=90°

Step-by-step explanation:

All the 4 triangles formed are isosceles. Since the diagonals of square bisect each other. Therefore angle QPR=45°,now we can get z as sum of all angles in a triangle is 180°.similarly x=45° and y and 45° are in a line therefore y=135°.

Answer 2

Let the centre angle be O

Angle POQ (Angle z) = 90

Let angle OPQ = a

POQ is a triangle

a + 90 + 45 = 180

a = 45

Angle SPO + Angle OPQ = 90

SPO = 90 - 45

Angle SPO = 45

SP and RQ are parallel,

So angle SPO = Angle OPQ

Angle x = 45

Therefore angle SRO = angle OSR = 45

Angle SOR = Angle z = 90

Angle SOR + Angle OSR = Angle y

90 + 45 = Angle y

Angle y = 135

x = 45

y = 135

z = 90

Hope it helps

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