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Charra [1.4K]
3 years ago
14

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.

Mathematics
2 answers:
vredina [299]3 years ago
8 0

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°

Arte-miy333 [17]3 years ago
4 0

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 \°

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