Question

in the figure below, line l and line m are parallel the measure of angle one equals 56°, and the measure of angle 2 equals 66°. what is the measure of angle 3?

Answer 1

Answer: the answer would be 34 (a)

Step-by-step explanation: Angle one equals 56 and and angle 4 is also 56. so then you would figure that angle 3 and 4 will equal 90 together. so you would do 90-56 which equals 34.

Answer 2

A.
`34^(\circ)`

Explanation:

We have been given a diagram. We are asked to find the measure of angle 3.

We can see that angle 1 and angle 6 are vertical angles, therefore, measure of angle 1 will be equal to measure of angle 6.

`m\angle 6=m\angle 1`

`m\angle 6=56^(\circ)`

We will find measure of angle 3 using angle sum property as:

`m\angle 3+m\angle 6+90^(\circ)=180^(\circ)`

`m\angle 3+56^(\circ)+90^(\circ)=180^(\circ)`

`m\angle 3+146^(\circ)=180^(\circ)`

`m\angle 3+146^(\circ)-146^(\circ)=180^(\circ)-146^(\circ)`

`m\angle 3=34^(\circ)`

Therefore, the measure of angle 3 is 34 degrees and option A is the correct choice.