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alexandr402 [8]
3 years ago
13

A same side interior angle of two parallel lines is 20° less than the other same side interior angle. Find the measures of these

two angles.
Mathematics
1 answer:
erma4kov [3.2K]3 years ago
6 0

Answer:

The measures of the two angles are 80 and 100

Step-by-step explanation:

Let m_1 and m_2 represent the two angles such that

m_1 = m_2 - 20

Required

Find m_1 and m_2

<em>The two angles of a same-side interior angle of parallel lines add up to 180;</em>

<em></em>

This implies that

m_1 + m_2 = 180

Substitute m_2 - 20 for m_1

m_1 + m_2 = 180 becomes

m_2 - 20 + m_2 = 180

Collect like terms

m_2  + m_2 = 180 + 20

2m_2 = 180 + 20

2m_2 = 200

Divide both sides by 2

\frac{2m_2}{2} = \frac{200}{2}

m_2 = \frac{200}{2}

m_2 = 100

Recall that m_1 = m_2 - 20

m_1 = 100 - 20

m_1 = 80

Hence, the measures of the two angles are 80 and 100

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