Question

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.

Answer 1

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 $m_2$

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

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