Angle Relationships Parallel Lines Two angles are complementary

Angle Relationships & Parallel Lines

Two angles are complementary if the sum of their measures is 90. 1 2

Find the measure of x. x 50°

Two angles are supplementary if the sum of their measures is 180. 1 2

Find the measure of each angle 2 x x+30

Two angles with a common side are adjacent. 1 2

Two lines in a plane will: n be parallel n coincide n or intersect.

When two lines intersect at right angles, they are called perpendicular lines.

When two lines intersect, pairs of vertical angles are formed. Vertical angles have the same measure.

If two parallel lines are cut by a third line, called the transversal, various pairs of angles are formed.

These angles are corresponding angles. Corresponding angles have the same measure.

These angles are alternate interior angles. Alternate interior angles have the same measure.

These angles are alternate exterior angles. Alternate exterior angles have the same measure.

Name the following pairs of angles.

Alternate Interior

Vertical

Alternate Exterior

Corresponding

Supplementary

Supplementary

1 3 5 7 6 2 4 8 Corresponding Angles: Angles on different lines with the same measure.

1 3 5 7 6 2 4 8 Alternating Interior Angles: Angles in-between the coplanar lines. Adjacent Angles: Share a vertex and a side but have no interior points in common.

Find the missing angle measures. 300 ? ? ?

180 Rule for Triangles - the sum of the interior angles of any triangle is always 180. b 80 a 40 40 x c + 80 + x = 180 120 + x = 180 x = 60

Find each angle below. 180° rule for triangles 2 y - 10 y + 14 = 63 88 ° 63° y+14 29 ° y - 20 2 y - 10 = 88 y - 20 = 29 180 (y + 14) + (2 y - 10) + (y - 20) = 180 4 y - 16 = 180 +16 4 y = 196 y = 49

What are the measures of the base angles of an isosceles triangle in which the vertex angle measures 45° ? x + 45 = 180 2 x = 135 45 x = 67 ½ ° x x The base angle are congruent

Find the missing angle. 40 40 + 48 + x = 180 x 88 + x = 180 92° x = 92 132 a 48 a + 132 = 180 a = 48

180 Rule for Triangles - the sum of the interior angles of any triangle is always 180. b 80 40 a 40 x c + 80 + x = 180 120 + x = 180 x = 60

Find each angle below. 2 y - 10 y + 14 = 63 2 y - 10 = 88 y - 20 = 29 y+14 y - 20 180 (y + 14) + (2 y - 10) + (y - 20) = 180 4 y - 16 = 180 +16 4 y = 196 y = 49

Find the missing angle. x 40 132

Find the missing angle. 119 124 x