Question

Give 1) the angle relationship for each set of angles and 2) themeasure of the missing angle.

Answer 1

1.

Relationship: Supplementary

m

2.

Relationship: Complementary

m

3.

Relationship: Vertical Angles

m

4.

Relationship: Consecutive Angles

m

Explanation:

1.

These two angles are supplementary, the sum of both is equal to 180 °, therefore

`\begin{gathered} 180=x+57 \\ x=180-57 \\ x=123\text{\degree} \end{gathered}`

2.

These two angles are complementary, the sum of both is equal to 90 °, therefore

`\begin{gathered} 90=x+26 \\ x=90-26 \\ x=64\text{\degree} \end{gathered}`

3.

These two angles are vertical angles, which means that they share a vertex, which means that the measure is the same.

TVZ = 89°

4.

In this case they are two angles forming a larger angle, they are consecutive angles, the resulting angle in the sum of both angles:

`\begin{gathered} x=63+48 \\ x=111\text{\degree} \end{gathered}`