Question

1. ( mangle5 = mangle6 ) 15. ( = 2(47) - 21 = 94 ) ( 07^circ )

Explanation:

Step1: Analyze the angle sum

The straight line forms a 180° angle, and there's a right angle (90°) between ∠5 and ∠6. So the sum of ∠5 and ∠6 is \(180^\circ - 90^\circ = 90^\circ\).

Step2: Use \(m\angle5 = m\angle6\)

Let \(m\angle5 = m\angle6 = x\). Then \(x + x = 90^\circ\), which simplifies to \(2x = 90^\circ\).

Step3: Solve for \(x\)

Divide both sides by 2: \(x=\frac{90^\circ}{2}=45^\circ\). So \(m\angle5 = m\angle6 = 45^\circ\).

Answer:

\(m\angle5 = 45^\circ\), \(m\angle6 = 45^\circ\)