Question

find each measure.

1. ( mangle1 )
2. ( mangle2 )
3. ( mangle3 )
4. ( mangle4 )
5. ( mangle5 )
6. ( mangle6 )

Explanation:

Step1: Use the property of right - angled triangle

In the right - angled triangle with angle \(35^{\circ}\) and \(\angle1\), since the sum of angles in a right - angled triangle is \(90^{\circ}\).
\(\angle1 + 35^{\circ}=90^{\circ}\)

Step2: Solve for \(\angle1\)

\(\angle1=90^{\circ}- 35^{\circ}\)

Step3: Use the property of right - angled triangle for \(\angle5\)

In the right - angled triangle with angle \(28^{\circ}\) and \(\angle5\), since the sum of angles in a right - angled triangle is \(90^{\circ}\).
\(\angle5 + 28^{\circ}=90^{\circ}\)

Step4: Solve for \(\angle5\)

\(\angle5=90^{\circ}-28^{\circ}\)

Answer:

\(m\angle1 = 55^{\circ}\), \(m\angle5=62^{\circ}\)