You have learned about angles before (previous course)

• Examine relationships between pairs of angles.

• Examine relationships of angles formed by parallel lines and a transversal.

• perpendicular lines

• vertical angles

• adjacent angles

• complementary angles

• supplementary angles

• parallel lines

Lines that intersect to form right angles

Two pairs of opposite angles formed by two intersecting lines. The angles are congruent.

Two angles that have the same vertex, share a common side, and do not overlap

Two angles whose sum is 90°

Two angles whose sum is 180°

Two lines in a same plane that do not intersect

• transversal

• alternate interior angles

• alternate exterior angles

• corresponding angles

A line that intersects two parallel lines to form eight angles

Nonadjacent interior angles found on opposite sides of the transversal. In parallel lines, these are congruent.

Nonadjacent exterior angles found on opposite sides of the transversal. In parallel lines, these are congruent.

Angles that have the same position on two different parallel lines cut by a transversal. These angles are congruent.

Find a Missing Angle Measure

A. Jun is cutting a tile. Classify the relationship of a and b.

Answer: The angles are complementary. The sum of their measures is 90°.

Find a Missing Angle Measure

B. If ma = 53°, what is the measure of b?

mb + 53 = 90 Write the equation.

mb + 53 – 53 = 90 – 53 Subtract 53 from each side.

mb = 37 Simplify.

Answer: mb = 37°

A. A

B. B

C. C

D. D

A. They are complementary.

B. They are supplementary.

C. They are congruent.

D. They are obtuse.

A. Elisa is cutting a piece of fabric. What is the relationship between a and b?

ab

A. A

B. B

C. C

D. D

A. 140°

B. 220°

C. 50°

D. 90°

B. If ma = 40°, what is mb?

ab

Find Measures of Angles Formed by Parallel Lines

Answer: Since 9 and 13 are corresponding angles, they are congruent.

A. Classify the relationship between 9 and 13.

Find Measures of Angles Formed by Parallel Lines

Answer: m11 = 75° and m15 = 75°

B. If m13 is 75°, find m11 and m15.

Since 13 and 11 are alternate interior angles, they are congruent. So, m11 = 75°.

11 and 15 are corresponding angles and are congruent. So, m15 = 75°.

A. A

B. B

C. C

D. D

A. They are corresponding and congruent.

B. They are adjacent and supplementary.

C. They are corresponding and supplementary.

D. They are adjacent and congruent.

A. What is the relationship between 1 and 5?

A. A

B. B

C. C

D. D

A. 12°

B. 22°

C. 78°

D. 102°

B. If m3 = 78°, what is m7?

Use Algebra to Find Missing Angle Measures

ALGEBRA Angles DEF and WXY are complementary angles, with mDEF = 2x and mWXY = 3x – 20. Find the measures of DEF and WXY.

mDEF + mWXY = 90 Complementary angles

2x + 3x – 20 = 90 Replace mDEF with 2x and mWXY with 3x – 20.

Step 1 Find the value of x.

Use Algebra to Find Missing Angle Measures

Combine like terms.

Add 20 to each side.

Simplify.

Divide each side by 5.

Simplify.

Use Algebra to Find Missing Angle Measures

Answer: mDEF = 44° and mWXY = 46°

Step 2 Replace x with 22 to find the measure of each angle.

mDEF = 2x mWXY = 3x – 20

= 2(22) or 44

= 3(22) – 20 or 46

A. A

B. B

C. C

D. D

A. mABC = 12° and mRST = 78°

B. mABC = 20° and mRST = 70°

C. mABC = 30° and mRST = 60°

D. mABC = 30° and mRST = 70°

Angles RST and ABC are complementary angles with mRST = 3x and mABC = x + 10. What are the measures of ABC and RST?