Question

exit ticket
complete each statement about the figure.

1. ∠1 and ∠_ are complementary angles.
2. ∠5 and ∠_ are supplementary angles.
3. ∠1 and ∠2 ______ a linear pair of angles.
4. the ____ and ____ lines in the figure are perpendicular.
5. if m∠2 = 27° and m∠3 = 59°, m∠1 =__, m∠4 = and m∠5 = __.

Explanation:

Step1: Recall complementary angles definition

Complementary angles add up to 90°. In the figure, ∠1 and ∠2 are complementary as they form a right - angled corner.

Step2: Recall supplementary angles definition

Supplementary angles add up to 180°. ∠5 and ∠6 are supplementary as they form a straight - line.

Step3: Recall linear - pair definition

A linear pair of angles are adjacent and supplementary. ∠1 and ∠2 are not a linear pair as they do not form a straight - line.

Step4: Identify perpendicular lines

The vertical and horizontal lines in the figure are perpendicular as they intersect at 90°.

Step5: Calculate angle measures

Since ∠1 and ∠2 are complementary, if \(m\angle2 = 27^{\circ}\), then \(m\angle1=90^{\circ}- 27^{\circ}=63^{\circ}\). Since ∠3 and ∠4 are vertical angles, \(m\angle4 = m\angle3 = 59^{\circ}\). Since ∠5 is a right - angle, \(m\angle5 = 90^{\circ}\).

Answer:

1. 2
2. 6
3. are not
4. vertical, horizontal
5. \(63^{\circ}\), \(59^{\circ}\), \(90^{\circ}\)