Question

1. find the value of x.

(6x + 7)° (8x - 17)°

1. find the value of x.

(11x - 15)° (5x - 13)°

Explanation:

Step1: Identify vertical - angles property

Vertical angles are equal. For question 11, \(6x + 7=8x - 17\).

Step2: Solve the equation for \(x\)

Subtract \(6x\) from both sides: \(7 = 8x-6x - 17\), which simplifies to \(7 = 2x-17\). Then add 17 to both sides: \(7 + 17=2x\), so \(24 = 2x\). Divide both sides by 2: \(x=\frac{24}{2}=12\).

Step3: For question 12, use the linear - pair property

The sum of angles in a linear - pair is \(180^{\circ}\). So \((11x - 15)+(5x - 13)=180\).

Step4: Combine like terms

\(11x+5x-15 - 13 = 180\), which gives \(16x-28 = 180\).

Step5: Solve for \(x\)

Add 28 to both sides: \(16x=180 + 28=208\). Then divide both sides by 16: \(x=\frac{208}{16}=13\).

Answer:

1. \(x = 12\)
2. \(x = 13\)