Question

given the diagram, if ( mangle1 = 40^{circ} ) then ----------. choose all that apply.
( mangle2 = 40^{circ} )
( mangle2 = 90^{circ} )
( mangle2 = 50^{circ} )
angles 1 and 2 are supplementary
angles 1 and 2 are complementary

Explanation:

Step1: Recall the definition of complementary angles

Complementary angles are two angles whose sum is \(90^{\circ}\).

Step2: Calculate \(m\angle2\)

Given \(m\angle1 = 40^{\circ}\), and since \(\angle1\) and \(\angle2\) are complementary (sum to \(90^{\circ}\)), we use the formula \(m\angle2=90^{\circ}-m\angle1\).
Substitute \(m\angle1 = 40^{\circ}\) into the formula: \(m\angle2 = 90^{\circ}-40^{\circ}=50^{\circ}\).

Answer:

\(m\angle2 = 50^{\circ}\), Angles 1 and 2 are complementary.