Question

mathematics instructional plan - grade 8
complementary angles
\\( \angle 1 \\) and \\( \angle 2 \\) are complementary angles. measure angle 1: \\( m \angle 1= \\) _
now use your knowledge of complementary and corresponding angles to find the other missing
angles.
\\( m \angle 2= \\) _ \\( m \angle 3= \\) _ \\( m \angle 4= \\) _ \\( m \angle 5= \\) _ \\( m \angle 6= \\) _
what is the relationship between the measures of complementary angles?
draw a pair of complementary angles.
write a definition of complementary angles.
use your figure to test your definition. does your definition hold true? why, or why not? write
a new definition below if necessary.

Explanation:

Step1: Find \(m\angle2\)

Since \(\angle1\) and \(\angle2\) are complementary, \(m\angle1 + m\angle2=90^{\circ}\). Given \(m\angle1 = 42^{\circ}\), then \(m\angle2=90 - 42=48^{\circ}\)

Step2: Find \(m\angle3\)

\(\angle2\) and \(\angle3\) are vertical angles. Vertical angles are equal. So \(m\angle3 = m\angle2 = 48^{\circ}\)

Step3: Find \(m\angle4\)

\(\angle3\) and \(\angle4\) are complementary. \(m\angle4=90 - 48 = 42^{\circ}\)

Step4: Find \(m\angle5\)

\(\angle4\) and \(\angle5\) are vertical angles. So \(m\angle5=m\angle4 = 42^{\circ}\)

Step5: Find \(m\angle6\)

\(\angle6\) is a right - angle. So \(m\angle6 = 90^{\circ}\)

Answer:

\(m\angle2 = 48^{\circ}\), \(m\angle3 = 48^{\circ}\), \(m\angle4 = 42^{\circ}\), \(m\angle5 = 42^{\circ}\), \(m\angle6 = 90^{\circ}\)