Question

given the figure below, find the values of x and z.
(12x + 10)° (10x + 22)°
z°
x=
z=

Explanation:

Step1: Use vertical angles property

Vertical angles are equal. So, \(12x + 10=10x + 22\).
Subtract \(10x\) from both sides: \(12x-10x + 10=10x-10x + 22\), which simplifies to \(2x+10 = 22\).
Subtract \(10\) from both sides: \(2x+10 - 10=22 - 10\), so \(2x=12\).
Divide both sides by \(2\): \(x=\frac{12}{2}=6\).

Step2: Find \(z\)

Use the linear - pair property. If two angles form a linear pair, their sum is \(180^{\circ}\).
Substitute \(x = 6\) into \(10x + 22\): \(10\times6+22=60 + 22=82^{\circ}\).
Then \(z+82 = 180\).
Subtract \(82\) from both sides: \(z=180 - 82=98\).

Answer:

\(x = 6\)
\(z = 98\)