Question

Abcd is a cyclic quadrilateral find the angles of a cyclic quadrilateral

Answer 1

3y-5-7x+5=180

3y-7x=180----------1

4y+20-4x=180

4y-4x=160

dividing each term by 4

y-x=40

y=40+x-------------2

putting 1 in2

3(40+x)-7x=180

120+3x-7x=180

-4x=60

x= -15

y=40-15

=25

so,

A=4*25 +20

=120

B=3*25-5

=70

C=-4*-15

=60

D=-7*-15+5

=110

Answer 2

Step-by-step explanation:

Given:

• ABCD is a cyclic quadrilateral.

To Find:

• All angles of the cyclic quadrilateral.

Solution: We know that the sum of opposite angles of the cyclic quadrilateral is of 180°.

∴ ∠A + ∠B = 180°

$\small\implies{\sf }$ 4y+20−4x=180

$\small\implies{\sf }$ 4y−4x=180−20

$\small\implies{\sf }$ 4y−4x=160 [ Divide both sides by 4 ]

$\small\implies{\sf }$ 4y/4 – 4x/4 = 160/4

$\small\implies{\sf }$ x – y = – 40 .......(1)

∠B + ∠D = 180°

$\small\implies{\sf }$ 3y – 5 – 7x + 5 = 180

$\small\implies{\sf }$ – 7x + 3y = 180 + 5 – 5

$\small\implies{\sf }$ – 7x + 3y = 180° ......(2)

★ Multiply equation (1) by 3 we will get ★

$\small\implies{\sf }$ 3(x – y) = 3(–40)

$\small\implies{\sf }$ 3x – 3y = –120.......(3)

• Adding equations 2 and 3 •

$\small\implies{\sf }$ – 7x + 3x = 180 – 120

$\small\implies{\sf }$ – 4x = 60

$\small\implies{\sf }$ x = 60/–4 = – 15

• Put the value of x in equation 1 •

$\small\implies{\sf }$ x – y = – 40

$\small\implies{\sf }$ – 15 – y = – 40

$\small\implies{\sf }$ – y = – 40 + 15

$\small\implies{\sf }$ – y = – 25

$\small\implies{\sf }$ y = 25

• ∠A = 4y + 20 = 4(25)+20 = 100+20 = 120°

• ∠B = 3y – 5 = 3(25)–5 = 75–5 = 70°

• ∠C = –4x = –4(–15) = 60°

• ∠D = –7x + 5 = –7(–15)+5 = 105+5 = 110°