Question

Given m∠1=65°, find the measure of each missing angle. Give your reasoning.

Answer 1

Answer:

$m_2= 115$

$m_3 = 65$

$m_4 = 115$

$m_5 = 65$

$m_6 = 115$

$m_7 = 65$

$m_8 = 115$

Step-by-step explanation:

See attachment for complete question.

Given

$m_1 = 65$

Required

Determine the missing angles

m1 and m2 are supplementary angles.

Meaning that:

$m_1 +m_2 = 180$

Substitute 65 for m1

$65 +m_2 = 180$

$m_2= 180 - 65$

$m_2= 115$

m1 and m3 are vertically opposites.

m2 and m4 are also vertically opposites.

So:

$m_3 = m_1$

and

$m_4 = m_2$

i.e.

$m_3 = 65$

$m_4 = 115$

When parallel lines are traversed by a line, the corresponding angles are equal.

This means that:

$m_5 = m_1$

$m_6 = m_2$

$m_7 = m_3$

$m_8 = m_4$

Because they are all corresponding angles.

So:

$m_5 = 65$

$m_6 = 115$

$m_7 = 65$

$m_8 = 115$