Question

find ( mangle1 ).
24.
25.
26.
27.

Explanation:

24.

Step1: Use the property of complementary angles

Complementary angles sum to \(90^{\circ}\). Let \(m\angle1=x\). Then \(x + 75^{\circ}=90^{\circ}\).

Step2: Solve for \(x\)

\(x=90^{\circ}-75^{\circ}\)
\(x = 15^{\circ}\)

25.

Step1: Use the property of supplementary angles

Supplementary angles sum to \(180^{\circ}\). Let \(m\angle1=x\). If one of the angles is \(90^{\circ}\), then \(x+90^{\circ}=180^{\circ}\)

Step2: Solve for \(x\)

\(x=180^{\circ}-90^{\circ}\)
\(x = 90^{\circ}\)

26.

Step1: Use the property of angles in a right - angled system

The sum of angles around the intersection (excluding the right - angle) is \(90^{\circ}\). Let \(m\angle1=x\). Then \(x+62^{\circ}=90^{\circ}\)

Step2: Solve for \(x\)

\(x=90^{\circ}-62^{\circ}\)
\(x = 28^{\circ}\)

27.

Step1: Use the property of angles around a right - angled intersection

The sum of angles around the intersection (excluding the right - angle) is \(90^{\circ}\). Let \(m\angle1=x\). Then \(x + 10^{\circ}=90^{\circ}\)

Step2: Solve for \(x\)

\(x=90^{\circ}-10^{\circ}\)
\(x = 80^{\circ}\)

Answer:

1. \(15^{\circ}\)
2. \(90^{\circ}\)
3. \(28^{\circ}\)
4. \(80^{\circ}\)