Question

Lines x and y are parallel and are cut by the transversal b. If the measure of angle 1 is 57°, what is the measure of angle 6? Explain the relationship between the two angles.

Answer 1

Answer:

$\angle6=123$

Step-by-step explanation:

Given

Lines x and y

Transversal b

$\angle 1 = 57$

Required

Find $\angle 6$

From the attachment, $\angle1$ and $\angle7$ are vertically opposite.

This means that

$\angle 1 =\angle 7 = 57$

Similarly

$\angle 7$  and $\angle 6$ are supplementary angles

So:

$\angle7 + \angle6=180$

Make $\angle6$ the subject

$\angle6=180-\angle7$

$\angle6=180-57$

$\angle6=123$

The relationship between $\angle1$ and $\angle6$ is that they are supplementary angles because:

$\angle6+ \angle1=180$