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

Answer:

see explanation

Step-by-step explanation:

Let ∠4 be x then ∠6 is $\frac{1}{8}$ x

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

x + $\frac{1}{8}$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°

Answer 2

Answer:

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

Step-by-step 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

$m \angle 6 = \frac{1}{8} \times m \angle 4$

But,

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

Replacing this, we have

$180\° - m \angle 4=\frac{1}{8}(m \angle 4)\\(\frac{1}{8}+1) (m\angle 4)=180\°\\\frac{9}{8}(m\angle 4) = 180 \°\\ m \angle 4 = \frac{180(8)}{9}= 160\°$

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

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