Lesson One · Part 3

Worked Examples with Full Solutions

Read the question first, try it on paper, then reveal the model answer. Every solution follows the same three moves: name the relation, write the equation, solve for the unknown.

Solved examples

Example 1Reflex angles

Find the measure of a reflex angle

In the figure, m (∠ABC) = 130°.

Find the measure of reflex ∠ABC.

Example 2Equations

Find the value of X

1 Two adjacent angles with perpendicular outer sides: (3X + 15)° fills a right angle.

2 Angles around a point: (3X − 1)° + (X + 5)° = 360°

Example 3Complement / supplement

Complete the table

Complete: angle · complementary angle · supplementary angle.

Example 4Ratios

Angles given as a ratio

If m(∠A) : m(∠B) = 7 : 3 and the two angles are complementary, find m(∠A) and m(∠B).

If m(∠A) : m(∠B) = 4 : 1 and the two angles are supplementary, find m(∠B).

Example 5Straight line

Adjacent supplementary angles

In the figure, B ∈ AC and m(∠ABE) = 80°, m(∠EBD) = 30°.

Find m(∠DBC).

Example 6Perpendicular

Adjacent complementary angles

In the figure, AC ⊥ AB, and the two adjacent angles are (7X + 2)° and (3X − 5)°.

Find the value of X.

Example 7Proof

Straight line or perpendicular?

1 Are BA and BC on a straight line, if the angles at B are 55°, 70° and 50°? Why?

2 Is DC ⊥ DA, if m(∠ADB) = 37° and m(∠BDC) = 53°? Why?

Example 8Bisector

Using an angle bisector

BC ⊥ BA, m(∠EBC) = 40°, and BD bisects ∠ABE.

Find m(∠ABD).

Try it yourself

For timed practice, open the activities and games section.