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.

see explanation

Step-by-step explanation:

Let ∠4 be x then ∠6 is x

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

x + 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°

Step-by-step explanation:

From the graph, we can say that

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

But,

Replacing this, we have

Then,

Therefore, the measures of these two angles are