MATH SOLVE

2 months ago

Q:
# Which relationship exists between the two angles? What is the value of x? Find the measure of each angle. A) vertical angles; x = 3; 76 degrees; 76 degrees B) alternate exterior angles; x = 5; 116 degrees; 64 degrees C) corresponding angles: x = 7; 156 degrees; 156 degrees D) alternate exterior angles; x = 5; 116 degrees; 116 degrees Eliminate

Accepted Solution

A:

Answer:Option D.Step-by-step explanation:Diagram is missing, let as consider the diagram of this question is shown below.If a transversal line intersect two parallel lines, then the alternate exterior angles are equal.From the given figure it is clear that both angles alternate exterior angles. It means measure of both angles are equal.[tex]21x+11=20x+16[/tex]Subtract 20x from both sides.[tex]21x+11-20x=20x+16-20x[/tex][tex]x+11=16[/tex]Subtract 11 from both sides.[tex]x+11-11=16-11[/tex][tex]x=5[/tex]The value of x is 5.Measure of each angle is[tex]21x+11=21(5)+11=116^{\circ}[/tex][tex]20x+16=20(5)+16=116^{\circ}[/tex]Therefore, the correct option is D.