Question

find the m∠hjm in the diagram below.
(14x - 8)°
(8x+4)°
m∠hjm=

Explanation:

Step1: Identify vertical - angle property

Vertical angles are equal. So, \(14x - 8=8x + 4\).

Step2: Solve for \(x\)

Subtract \(8x\) from both sides: \(14x-8x - 8=8x-8x + 4\), which simplifies to \(6x-8 = 4\). Then add 8 to both sides: \(6x-8 + 8=4 + 8\), getting \(6x=12\). Divide both sides by 6: \(x=\frac{12}{6}=2\).

Step3: Find the measure of \(\angle HJM\)

Substitute \(x = 2\) into the expression for \(\angle HJM\) (we can use either \(14x - 8\) or \(8x + 4\)). Using \(14x - 8\), we have \(14\times2-8=28 - 8=20\).

Answer:

\(20^{\circ}\)