Question

4 find the value of y.
(3y + 1)° (8x - 61)° (6x - 13)°
6 find the value of y.
(9x + 42)° (15x)° (4y - 13)°
8 find the value of y.
(5y)° (13x - 33)° (10x)°
10 find the value of x.
(16x - 4)° 58° (9x - 6)°

Explanation:

4.

• Step1: Use vertical - angle property

Vertical angles are equal. So, \(6x - 13=8x - 61\).
\[

$$\begin{align*} 8x-6x&=61 - 13\\ 2x&=48\\ x& = 24 \end{align*}$$

\]

• Step2: Find \(y\) using another angle - relationship

\(3y + 1=6x - 13\) (vertical angles). Substitute \(x = 24\) into it.
\[

$$\begin{align*} 3y+1&=6\times24 - 13\\ 3y+1&=144 - 13\\ 3y+1&=131\\ 3y&=130\\ y&=\frac{130}{3} \end{align*}$$

\]

6.

• Step1: Use corresponding - angle property

Corresponding angles are equal. So, \(9x + 42=15x\).
\[

$$\begin{align*} 15x-9x&=42\\ 6x&=42\\ x& = 7 \end{align*}$$

\]

• Step2: Find \(y\) using another angle - relationship

\(4y-13 = 9x + 42\) (corresponding angles). Substitute \(x = 7\) into it.
\[

$$\begin{align*} 4y-13&=9\times7 + 42\\ 4y-13&=63+42\\ 4y-13&=105\\ 4y&=118\\ y&=\frac{59}{2} \end{align*}$$

\]

8.

• Step1: Use corresponding - angle property

Corresponding angles are equal. So, \(13x-33 = 10x\).
\[

$$\begin{align*} 13x-10x&=33\\ 3x&=33\\ x& = 11 \end{align*}$$

\]

• Step2: Find \(y\) using another angle - relationship

\(5y=10x\) (corresponding angles). Substitute \(x = 11\) into it.
\[

$$\begin{align*} 5y&=10\times11\\ y&=22 \end{align*}$$

\]

10.

• Step1: Use vertical - angle property

Vertical angles are equal. So, \(16x-4=9x - 6+58\).
\[

$$\begin{align*} 16x-9x&=- 6 + 58+4\\ 7x&=56\\ x&=8 \end{align*}$$

\]

Answer:

1. \(y=\frac{130}{3}\)
2. \(y=\frac{59}{2}\)
3. \(y = 22\)
4. \(x = 8\)