Question

pqrs is a rectangle, angle poq=112°,find angles X, y, z​

Answer 1

Explanation:

Given that:

PQRS is a rectangle,angle POQ=112°,find angles X, y, z

To find: angle x,y and z

Solution:

In figure ∆POQ is isosceles triangle

PO=PQ

$\angle \: OPQ + \angle POQ + \angle \: X = 180° \\ \\ \angle \: OPQ = \angle \: X \\ (angle \: opposite \: to \: equal \: sides \: are \: equal) \\ \\2 \angle \: X + 110° = 180° \\ \\ 2 \angle \: X = 180° - 110° \\ \\ 2 \angle \: X = 70° \\ \\ \angle \: X = 35°$

In ∆QPS, right angle at P

Apply angle sum property of triangle

$\angle \: X + \angle \: OPS + \angle \: Y = 180° \\ \\ 35° + 90° + \angle \: Y= 180° \\ \\ \angle \: Y= 180° - 125° \\ \\ \angle \: Y = 55°$

∆POQ and ∆OSR are congruent,thus isosceles

So,

$\angle \:Z = 35°$

Thus,

$\angle \: X = 35° \\ \\ \angle \: Y= 55° \\ \\ \angle \: Z= 35°$

Hope it helps you.