Question

The correspondence PQR⇔YZX between ΔPQR and ΔYZX is a similarity. If m∠P=60, m∠R=40, then m∠Z=80.State whether the given statement are true or false. Give reasons for your answer.

Answer 1

The given statement is true,

Explanation :- The correspondence PQR⇔YZX between ΔPQR and ΔYZX is a similarity.
m∠P = m∠Y
m∠Q = m∠Z
m∠R = m∠X
Given, m∠P = 60° = m∠Y
m∠R = 40° = m∠X

then, m∠X + m∠Y + m∠Z = 180°
m∠Z = 180° - (m∠X + m∠Y)
= 180° - (40° + 60°)
= 180° - 100°
= 80°

Answer 2

Since the triangles PQR and YZX

are similar, then they are equiangular.

Angle P = Angle Y = 60 degrees

Angle Q = Angle Z = 80 degrees

Angle R = Angle X = 40 degrees


Angle P + Angle Q + Angle R =
180degrees

Angle X + Angle Y+ Angle Z =
180degrees

Therefore the statement is true.

I hope this answer helps you