Question

If the measure of angle 2 is (5x+14) and angle 3 is (7x-14), what is the measure of angle 1 in degrees?

Answer 1

91

Explanation:

From the figure we can write the angle relationship as follows:

m\angle 1=m\angle 3m∠1=m∠3 [Vertical angles are congruent]

m\angle 2=m\angle 4m∠2=m∠4 [Vertical angles are congruent]

$$m\angle 2+m\angle 3=180\°$$ [Linear pair of angles have sum = 180°]

We are given:

$$m\angle 2=5x+14$$

$$m\angle 3=7x-14$$

We know, $$m\angle 2+m\angle 3=180\°$$

So, we have:

$$5x+14+7x-14=180$$

Solving for $$x$$

Combining like terms

$$12x=180$$

Dividing both sides by 12.

$$\frac{12x}{12}=\frac{180}{12}$$

$$x=15$$

Using $$x=15$$ to evaluate ∠3

$$m\angle 3 = 7(15)-14=105-14=91\°$$

We know $$m\angle 1=m\angle 3$$

∴ $$m\angle 1=91\°$$ (Answer)

Answer 2

D) 91°

Explanation:

From the figure we can write the angle relationship as follows:

`m\angle 1=m\angle 3` [Vertical angles are congruent]

`m\angle 2=m\angle 4` [Vertical angles are congruent]

`m\angle 2+m\angle 3=180\°` [Linear pair of angles have sum = 180°]

We are given:

`m\angle 2=5x+14`

`m\angle 3=7x-14`

We know,
`m\angle 2+m\angle 3=180\°`

So, we have:

`5x+14+7x-14=180`

Solving for
`x`

Combining like terms

`12x=180`

Dividing both sides by 12.

`(12x)/(12)=(180)/(12)`

`x=15`

Using
`x=15` to evaluate ∠3

`m\angle 3 = 7(15)-14=105-14=91\°`

We know
`m\angle 1=m\angle 3`

∴
`m\angle 1=91\°` (Answer)