Question

What is the value of q? Answer choices: 58 116 122 180

Answer 1

The opposite angles of the inscribed quadrilateral in the circle are supplementary.

angle q = 180 - 58
angle q = 122

Hope this helps :)

Answer 2

Answer:

122°

Step-by-step explanation:

We are supposed to find value of q

Refer the attached figure

Note: Opposite angles of cyclic quadrilateral are supplementary.

Supplementary angles: A pair of angles whose sum is 180°

So, $\angle ABC + \angle CDA = 180 ^{\circ}$ --1

$\angle ABC = 58 ^{\circ}$

$\angle CDA = y$

Substitute the values in 1

$58^{\circ} + y = 180 ^{\circ}$

$y = 180 ^{\circ}-58^{\circ}$

$y = 122^{\circ}$

Thus $\angle CDA = y=122^{\circ}$

Hence the value of q is 122°