Question

Lines AB and CD (if present in the picture) are straight lines. Find x. Give reasons to justify your solutions.

Answer 1

1. Angle Addition Postulate/Theorem

2. 90°

3. m<AOC; Vertical Angles

4. 90°; 110°

5. 20°

Explanation:

1. m<DOB = m<DOE + m<BOE (Reason: Angle Addition Postulate/Theorem)

2. m<DOB = 90° + x (Reason: Substitution)

Note: m<DOE is a right angle.

3. m<DOB = m<AOC (Reasons: Vertical Angles)

4. 90° + x = 110° (Reasons: Substitution)

5. x = 20° (Reasons: Algebra)

Note how we got 20° by applying algebra:

90° + x = 110°

Subtract 90° from both sides

90° + x - 90° = 110° - 90°

x = 20°