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

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

Answer :

akposevictor

Answer:

1. Angle Addition Postulate/Theorem

2. 90°

3. m<AOC; Vertical Angles

4. 90°; 110°

5. 20°

Step-by-step 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°

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