Question

Answer this please so i can do it thank

Answer 1

1. m∠AOB=180° Reason: straight line angles are supplementary

2. =m∠AOB Reason: they form the straight line angle ∠AOB

3. (5x-15°)+90°+2x=180°

4.
`5x+2x-15+90=180\\7x= 180-90+15\\7x=105\\(7x)/(7) =(105)/(7) \\x=15`

∴x=15°

Answer 2

1. Statement: m∠AOB = 180°

1. Reason: Straight Angle

2. Statement: m∠AOF + m∠FOG + m∠GOB = m∠AOB

2. Reason: Angle Addition Postulate

3. Statement: 5x - 15° + 90° + 2x = 180°

3. Reason: Substitution

4. Statement: x = 15°

4. Reason: Algebra

Explanation:

Part 1

Statement: m∠AOB = 180°

Reason: Straight Angle

Straight angle: An angle that is equal to 180°.

Part 2

Statement: m∠AOF + m∠FOG + m∠GOB = m∠AOB

Reason: Angle Addition Postulate

Angle Addition Postulate: When two or more angles are placed side by side such that they share a common vertex (and a common arm between each pair of angles), the sum of those angles will be equal to the total sum of the resulting angle.

Part 3

Statement: 5x - 15° + 90° + 2x = 180°

Reason: Substitution

Substitute the expression for each angle given in the diagram:

⇒ m∠AOF + m∠FOG + m∠GOB = m∠AOB

⇒ 5x - 15° + 90° + 2x = 180°

Part 4

Statement: x = 15°

Reason: Algebra

Solve the algebraic equation from part 3:

⇒ 5x - 15° + 90° + 2x = 180°

⇒ 5x + 2x + 90° - 15° = 180°

⇒ 7x + 75° = 180°

⇒ 7x + 75° - 75° = 180° - 75°

⇒ 7x = 105°

⇒ 7x ÷ 7 = 105° ÷ 7

⇒ x = 15°