Question

$overleftrightarrow{yg}$ is tangent to circle $o$ at point $y$. if $moverarc{yd} = 102^circ$, find $mangle dyg$.

answer

$mangle dyg = \square ^circ$

Explanation:

Step1: Recall tangent-chord angle theorem

The measure of an angle formed by a tangent and a chord is half the measure of its intercepted arc.

Step2: Identify intercepted arc

$\angle DYG$ intercepts arc $\widehat{YD}$, where $m\widehat{YD}=102^\circ$.

Step3: Calculate the angle measure

$m\angle DYG = \frac{1}{2} \times m\widehat{YD}$
$m\angle DYG = \frac{1}{2} \times 102^\circ$

Answer:

$51^\circ$