Question

4.

• ∠4 and ∠5 are complementary and the

m∠4 is 40°. find the remaining
measurements.
m∠1 = __, m∠2 = , m∠3 = __
m∠5 = __, m∠6 = __

Explanation:

Step1: Find \(m\angle5\)

Since \(\angle4\) and \(\angle5\) are complementary, \(m\angle4 + m\angle5=90^{\circ}\). Given \(m\angle4 = 40^{\circ}\), then \(m\angle5=90^{\circ}-40^{\circ}=50^{\circ}\).

Step2: Find \(m\angle3\)

\(\angle3\) is a right - angle (from the perpendicular lines), so \(m\angle3 = 90^{\circ}\).

Step3: Find \(m\angle1\)

\(\angle1\) and \(\angle5\) are vertical angles. Vertical angles are equal. So \(m\angle1=m\angle5 = 50^{\circ}\).

Step4: Find \(m\angle2\)

\(\angle2\) and \(\angle4\) are vertical angles. Vertical angles are equal. So \(m\angle2=m\angle4 = 40^{\circ}\).

Step5: Find \(m\angle6\)

\(\angle6\) and \(\angle3\) are supplementary (\(\angle3+\angle6 = 180^{\circ}\)). Since \(m\angle3 = 90^{\circ}\), then \(m\angle6=180^{\circ}-90^{\circ}=90^{\circ}\).

Answer:

\(m\angle1 = 50^{\circ}\), \(m\angle2 = 40^{\circ}\), \(m\angle3 = 90^{\circ}\), \(m\angle5 = 50^{\circ}\), \(m\angle6 = 90^{\circ}\)