In the diagram below, O is circumscribed about quadrilateral ABCD. what is the value of x?

Question

asked Sep 26, 2020 162k views

2 Answers

Nicholas C · Answer 1 · 2020-10-02T12:09:15+0000

Answer:

(D)
$x=104^(\circ)$

Explanation:

Given: It is given that circle O is circumscribed about quadrilateral ABCD such that ∠ABC=91° and ∠ADC=x-15°.

To find: the value of x.

Solution: It is given that circle O is circumscribed about quadrilateral ABCD such that ∠ABC=91° and ∠ADC=x-15°.

We know that the sum of opposite angles of the cyclic quadrilateral is 180°, therefore

${\angle}ABC+{\angle}ADC=180^(\circ)$

Substituting the given values, we have

$91^(\circ)+x-15^(\circ)=180^(\circ)$

$x+76^(\circ)=180^(\circ)$

$x=104^(\circ)$

thus, the value of x is
$104^(\circ)$ .

Hence, option D is correct.