In a cyclic quadrilateral $A B C D$ , $∠ A = 5 x, ∠ C = 4 x$ , the value of $x$ is:

12^{o}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

20^{o}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

48^{o}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

36^{o}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $20^{o}$
Opposite angles of a cyclic quadrilateral are supplementary

Then, $∠ A + ∠ C = 5 x + 4 x = 180^{\circ}$

$⟹$ $9 x = 180^{\circ}$

$⟹$ $x = 20^{\circ}$ .
Hence, option $B$ is correct.

Suggest Corrections

Similar questions

Q. In a cyclic quadrilateral

A B C D

∠ A = {(2 x + 11)}^{o}

∠ B = {(y + 12)}^{o}

∠ C = {(3 y + 6)}^{0}

and

∠ D = {(5 x - 25)}^{o}

, find the angles of the quadrilateral.

If $A B C D$ is a cyclic quadrilateral and $∠ A = 4 y + 20^{o}; ∠ B = 3 y - 5^{o}; ∠ C = - 4 x, ∠ D = - 7 x + 5^{o}$ , then find the value of $x$ and $y$ .

Q. In a cyclic quadrilateral

A B C D, 3 A = (x + 7)^{o} .3 B = (y + 8)^{o} .3 C = (3 y + 23)^{o}

and

3 D = (4 x + 12)^{o}

. Find all four angle of the cyclic quadrilateral.

Q. Two opposite angles of a cyclic quadrilateral are

4 x^{\circ}

and

5 x^{\circ}

, then the value of

x^{\circ}

is equal to

Q. Find the smallest angle of a cyclic quadrilateral

A B C D

in which

∠ A = (2 x - 10)^{o}, ∠ B = (2 y - 20)^{o}, ∠ C = (2 y + 30)^{o}

and

∠ D = (3 x + 10)^{o} .

Join BYJU'S Learning Program

In a cyclic quadrilateral ABCD, ∠A=5x,∠C=4x, the value of x is:

The correct option is B 20oOpposite angles of a cyclic quadrilateral are supplementary Then, ∠A+∠C=5x+4x=180∘ ⟹ 9x=180∘ ⟹x=20∘.Hence, option B is correct.

In a cyclic quadrilateral $A B C D$ , $∠ A = 5 x, ∠ C = 4 x$ , the value of $x$ is:

The correct option is B $20^{o}$
Opposite angles of a cyclic quadrilateral are supplementary

Then, $∠ A + ∠ C = 5 x + 4 x = 180^{\circ}$

$⟹$ $9 x = 180^{\circ}$

$⟹$ $x = 20^{\circ}$ .
Hence, option $B$ is correct.