Question

a carpenter is designing a side table. the horizontal portions of the table are parallel. to build the cross - sections, the carpenter needs to know the measures of the angles shown. the ( mangle3 = 100^{circ}) and ( mangle4 = 102^{circ}).
( mangle1=square^{circ})
( mangle2=square^{circ})

Explanation:

Step1: Use the property of alternate interior angles

When two parallel lines are cut by a transversal, alternate interior angles are equal. So, \(m\angle1 = 180^{\circ}-m\angle3\)

$$m\angle1=180 - 100=80^{\circ}$$

Step2: Use the property of alternate interior angles

Similarly, \(m\angle2 = 180^{\circ}-m\angle4\)

$$m\angle2=180 - 102 = 78^{\circ}$$

Answer:

\(m\angle1 = 80^{\circ}\), \(m\angle2=78^{\circ}\)