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In a cyclic quadrilateral ABCD, angle D = (x + 60) degrees and angle B = 6x degrees. Find the value of x.

May 3, 2026Mathematics

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Answer

\frac{120}{7}

17.14

5 steps

:
The figure shows a cyclic quadrilateral ABCD.

In a cyclic quadrilateral, opposite angles sum to $180^\circ$ .
Angles D and B are opposite.
$\angle D + \angle B = 180^\circ$
Substitute the given expressions for $\angle D$ and $\angle B$ from the image.
$(x^\circ + 60^\circ) + 6x^\circ = 180^\circ$
Combine like terms on the left side of the equation.
$7x^\circ + 60^\circ = 180^\circ$
Subtract $60^\circ$ from both sides of the equation.
$7x^\circ = 180^\circ - 60^\circ$ $7x^\circ = 120^\circ$
Divide by 7 to solve for $x$ .
$x = \frac{120}{7}$ $x \approx 17.1428$
The value of $x$ is $\boxed{\frac{120}{7}}$ or approximately $\boxed{17.14}$ .

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