Q16.

$\vec{D B}$ bisects $∠ A D C, m ∠ 1 = 5 x - 3, and m ∠ 2 = x + 25$ . Find the value of $x$ .

Verified

Answer

The number 7 represents itself as the value of $x$ .

1Step 1. Observe the given information.

The given information represents $\vec{D B}$ as a bisector which means the angles bisects by the line $\vec{D B}$ are equal to each other.

2Step 2. Make an equation by using the observation.

Equate the measurement of angles bisects by the line $\vec{D B}$ equal to each other. The angles are $∠ 1$ and $∠ 2$ .

$m ∠ 1 = m ∠ 2$

3Step 3. Determine the number that represents the value of x by using the obtained equation.

Substitute the value of $m ∠ 1$ and $m ∠ 2$ into the equation $m ∠ 1 = m ∠ 2$ and determine the number that represents the value of $x$ .

$\begin{matrix} 5 x - 3 = x + 25 \\ 5 x - x = 25 + 3 \\ 4 x = 28 \\ x = \frac{28}{4} \\ x = 7 \end{matrix}$