Question

1. find the value of x given ( mangle sar = (7x + 7)^circ ) and ( mangle sqr = (9x - 7)^circ ).

Explanation:

Step1: Identify congruent inscribed angles

Angles $\angle SAR$ and $\angle SQR$ intercept the same arc $\overset{\frown}{SR}$, so they are congruent.
$m\angle SAR = m\angle SQR$

Step2: Substitute given angle expressions

Replace angles with their algebraic forms.
$7x + 7 = 9x - 7$

Step3: Isolate x variable

Subtract $7x$ from both sides, then add 7 to both sides.
$7 + 7 = 9x - 7x$
$14 = 2x$

Step4: Solve for x

Divide both sides by 2.
$x = \frac{14}{2}$

Answer:

$7$