Question

Given that the measure of angle 6 is 1/8 of measure of angle 4. Find the measures of these two angles if a∥b.

Answer 1

`m \angle 4 = 160 \°\\m \angle 6 = 20 \°`

Explanation:

From the graph, we can say that

`m \angle 6 + m \angle 4 = 180 \°`

Because they are consecutive interior angles, and they sum 180° by definition. So, the reason of third statement is "by definition of consecutive interior angles".

We already know that

`m \angle 6 = (1)/(8) * m \angle 4`

But,

`m \angle 6 + m \angle 4 = 180 \°\\m \angle 6 = 180\° - m \angle 4`

Replacing this, we have

`180\° - m \angle 4=(1)/(8)(m \angle 4)\\((1)/(8)+1) (m\angle 4)=180\°\\(9)/(8)(m\angle 4) = 180 \°\\ m \angle 4 = (180(8))/(9)= 160\°`

Then,

`m \angle 6 + m \angle 4 = 180 \°\\m \angle 6 + 160\° =180\°\\m \angle 6 = 180-160=20`

Therefore, the measures of these two angles are

`m \angle 4 = 160 \°\\m \angle 6 = 20 \°`

Answer 2

see explanation

Explanation:

Let ∠4 be x then ∠6 is
`(1)/(8)` x

∠4 and ∠6 are same side interior angles and are supplementary, thus

x +
`(1)/(8)`x = 180

Multiply through by 8 to clear the fraction

8x + x = 1440, that is

9x = 1440 ( divide both sides by 9 )

x = 160

Hence ∠4 = 160° and ∠6 = 160° ÷ 8 = 20°