Question

ABCD is a cyclic quadrilateral such that

∠A = 90°, ∠B = 70°, find ∠C and∠D .​

Answer 1

Answer:

∠C=90°and ∠D=110

Step-by-step explanation:

we know that,

Opposites angles of a cyclic quad. are supplementary

so, ∠A+∠C=180

➨90+∠C=180

➨∠C=180-90

➨∠C=90

Smilarly, ∠B+∠D=180

➨70+∠D=180

➨∠D=180-70

➨∠D=110

Hence, ∠C=90°and ∠D=110°

Answer 2

Answer:

∠C = 90° and ∠D = 110°

Given :

A cyclic quadrilateral ABCD in which :

1. ∠A = 90°
2. ∠B = 70°

To find:

1. ∠C &
2. ∠D

Proof:

• P.F.A the figure below

According to the question.

• ∠A + ∠C = 180 °

[In a cyclic quadrilateral, the sum of opposite angles = 180 °]

⇒ 90° + ∠C = 180 °                                       [ ∠A = 90°, Given ]

⇒ ∠C = (180 - 90)°

⇒ ∠C = 90°

Similarly,

• ∠B + ∠D = 180 °

⇒ 70 +  ∠D = 180 °

⇒ ∠D = ( 180- 70 )°

⇒ ∠D = 110°

Hence, ∠C = 90° and ∠D = 110°

Proved.

Hope you got that.

Thank You.