Question

If ∠8 measures 132°, what is the sum of the measures of ∠1 and ∠4?

a.
132°
b.
264°
c.
96°
d.
180°

Answer 1

m<8 = m<4 = m<1 = 132
so m<4 + m<1 = 132 + 132 = 264

answer is b.
264°

Answer 2

b. 264°

Explanation:

In the given diagram,

∠8 and ∠4 are corresponding angles on parallel lines by same transversal,

Thus, by the corresponding angle theorem,

m∠8 = m∠4

Given, m∠8 = 132°

By substitution,

⇒ m∠4 = 132°

Now, ∠4 and ∠1 are vertical opposite angles,

By vertically opposite angle theorem,

Thus, m∠4 = m∠1

⇒ m∠1 = 132°

Hence, m∠1 + m∠4 = 132° + 132° = 264°

Option 'b' is correct.