Question

PQRS is rhombus with ∠QPS = 50º, Find angles a and b of figure

Answer 1

Answer:

Step. 1 find angle PQR ( QPS and PQR are supplementary)

step 2 divide it by 2 to get angle RQS

this is because the 2 triangles SPQ and QRS are congruent

therefore Angle RQS = PQS = 1/2 PQR

the answer is -> 65°

Answer 2

Step-by-step explanation:

∠TRV=180

∘

−∠UVR=180

∘

−114

∘

=66

∘

(adjacent angles of a rhombus)

∠SRU=∠SRT+

2

1

∠TRV=42

∘

+33

∘

=75

∘

∠QPS=∠SRU=75

∘

(opposite angles of a parallelogram)

(ii) ∠PDQ=∠PDN−∠QDN=90

∘

−31

∘

=59

∘

∠PQD=180

∘

−∠QPS−∠PDQ=180

∘

−75

∘

−59

∘

=46

∘

(angles of a triangle)

(iii) ∠DQN=∠PDQ=59

∘

(alternate angles of transversal)

∠MQN=180

∘

−∠DQN=180

∘

−59

∘

=121

∘

(angles on a straight line)

∴ ∠QPS=75

∘

, ∠PQD=46

∘

and ∠MQN=121

∘

[C