Question

find the values of x and y. x = y = save answer

Explanation:

Step1: Find the measure of angle $\angle BGD$

Since $\angle BGD$ is a right - angle, $\angle BGD = 90^{\circ}$.

Step2: Use the angle - sum property of angles around a point

The sum of angles around point $G$ is $360^{\circ}$. The non - overlapping angles around $G$ are $49^{\circ}$, $90^{\circ}$, $(12x + 5)^{\circ}$ and the arc measure $128^{\circ}$.
We know that the measure of an arc is equal to the measure of the central angle that subtends it. So, $49^{\circ}+90^{\circ}+(12x + 5)^{\circ}+128^{\circ}=360^{\circ}$.
First, simplify the left - hand side:
$49 + 90+12x + 5+128=360$.
$272+12x=360$.
Subtract 272 from both sides:
$12x=360 - 272$.
$12x = 88$.
$x=\frac{88}{12}=\frac{22}{3}$.

Step3: Find the value of $y$

We know that $\angle DGE$ and the arc measure $128^{\circ}$ are related. Also, $\angle BGD = 90^{\circ}$, $\angle BGC=49^{\circ}$.
The sum of $\angle BGC+\angle CGD+\angle DGE = 180^{\circ}$ (since they form a straight - line).
We know that $\angle CGD$ is the central angle corresponding to the arc of measure $128^{\circ}$, so $\angle CGD = 128^{\circ}$.
$\angle DGE=y^{\circ}$.
$49^{\circ}+128^{\circ}+y^{\circ}=180^{\circ}$.
$y^{\circ}=180^{\circ}-(49^{\circ}+128^{\circ})$.
$y^{\circ}=180^{\circ}-177^{\circ}$.
$y = 3$.

Answer:

$x=\frac{22}{3}$
$y = 3$