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:
A. [tex]34^{\circ}[/tex]
Step-by-step 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.
[tex]m\angle 6=m\angle 1[/tex]
[tex]m\angle 6=56^{\circ}[/tex]
We will find measure of angle 3 using angle sum property as:
[tex]m\angle 3+m\angle 6+90^{\circ}=180^{\circ}[/tex]
[tex]m\angle 3+56^{\circ}+90^{\circ}=180^{\circ}[/tex]
[tex]m\angle 3+146^{\circ}=180^{\circ}[/tex]
[tex]m\angle 3+146^{\circ}-146^{\circ}=180^{\circ}-146^{\circ}[/tex]
[tex]m\angle 3=34^{\circ}[/tex]
Therefore, the measure of angle 3 is 34 degrees and option A is the correct choice.
