15. find the values of x and y.
(18y + 5)°
(10x - 61)°
(x + 10)°

Question

Accepted Answer

# Explanation:
## Step1: Use vertical angles property
Vertical angles are equal. So, $10x - 61=x + 10$
$$
\begin{align*}
10x-x&=10 + 61\
9x&=71\
x&=\frac{71}{9}\approx7.89
\end{align*}
$$
## Step2: Use linear - pair property
$(18y + 5)+(10x - 61)=180$
Substitute $x = 7.89$ (or $\frac{71}{9}$) into the equation:
$$
\begin{align*}
18y+5+10\times\frac{71}{9}-61&=180\
18y+5+\frac{710}{9}-61&=180\
18y+\frac{45 + 710-549}{9}&=180\
18y+\frac{206}{9}&=180\
18y&=180-\frac{206}{9}\
18y&=\frac{1620 - 206}{9}\
18y&=\frac{1414}{9}\
y&=\frac{1414}{9\times18}=\frac{707}{81}\approx8.73
\end{align*}
$$

# Answer:
$x=\frac{71}{9}$, $y = \frac{707}{81}$

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QUESTION IMAGE

Question

Explanation:

Step1: Use vertical angles property

Step2: Use linear - pair property

Answer: