Question

Lines

AB
and
CD
(if present in the picture) are straight lines. Fill in the blank to find x.

Statement Reason
1. m∠AOC +m∠COE +m∠______ = m∠ ______ _________________________
2. m∠AOB = ________ _________________________
3. m∠EOB = ________ _________________________
4. x + ______ +90°=180°
Substitution
5. x = ________ Algebra

Answer 1

x = 30

Explanation:

Since AB is a straight line then

∠AOB + ∠COE + ∠EOB = 180° ← substitute values

x + 2x + 90 = 180 ( subtract 90 from both sides )

3x = 90 ( divide both sides by 3 )

x = 30

Answer 2

`x=30^(\circ)`

Explanation:

We are given that lines AB and CD are straight lines.

We have to fill in the blank space to find x.

1.
`m\angle AOC+m\angle COE+m\angle EOB=m\angle AOB`

By substitution

2.
`m\angle AOB=180^(\circ)`

Because angle AOB is a straight angle and measure of angle AOB=180 degrees.

3.
`m\angle EOB=90^(\circ)`

Because it is right angle and measure of right angle is 90 degrees.

4.
`x+2x+90=180`

By substitution

5.
`3x=180-90=90`

`x=(90)/(3)=30^(\circ)`