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Sum of Opposite Angles of a Cyclic Quadrilateral

ABCD is a cyc...

Question

ABCD is a cyclic quadrilateral such that ∠A = (4y + 20)°, ∠B = (3y − 5)°, ∠C = (−4x)° and ∠D = (7x + 5)°. Find the four angles.

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Solution

We know that the sum of the opposite angles of cyclic quadrilateral is .in the cyclic quadrilateral angles and and angles and pairs of opposite angles

Therefore

and

By substituting and we get

Divide both sides of equation by 4 we get

By substituting and we get

By multiplying equation by 3 we get

By subtracting equation from we get

By substituting in equation we get

The angles of a cyclic quadrilateral are

Hence the angles of quadrilateral are

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Similar questions

ABCD is a cyclic quadrilateral such that $∠ A = (4 y + 20)^{\circ}, ∠ B = (3 y - 5)^{\circ}, ∠ C = (4 x)^{\circ} a n d ∠ D = (7 x + 5)^{\circ}$ . Find the four angles.

A B C D

is a cyclic quadrilateral such that

∠ A = (4 y + 20), ∠ B = (3 y - 5), ∠ C = (- 4 x)

∠ D = (7 x + 5)

. Find the four angles.

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. Find the angles of a cyclic quadrilateral ABCD in which

∠ A = (4 x + 20) °, ∠ B = (3 x - 5) °, ∠ C = (4 y) ° and ∠ D = (7 y + 5) ° .

Q. In a cyclic quadrilateral ABCD, it is given that

∠ A = {(2 x + 4)}^{\circ}, ∠ B = {(y + 3)}^{\circ}, ∠ C = {(2 y + 10)}^{\circ} and ∠ D = {(4 x - 5)}^{\circ}

.
Find the four angles.

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