Question

What are the measures of Angles d, e, and f? Show your work and explain your answers. (10 points)

Part A - Find the measure of angle d showing all work and reasoning. (3 points)

Part B - Find the measure of angle e showing all work and reasoning. (3 points)

Part C - Find the measure of angle f showing all work and reasoning. (3 points)

Part D - What does the box mean in the triangle with angles e and d? (1 point)

Answer 1

Part A - Angle d is 29º

Part B - Angle e is 61º

Part C - Angle f is 95º

Part D - the box represents a 90º angle

Explanation:

Angle d is 29º because of the vertical angles theorem

Angle e is 61º because if you take into account that it tells you one of the angles is 90º, you'll add d, which is 29º, to that in order to get 119. Then you'll subtract 119 from 180, as all the angles in a triangle must have a sum of 180º degrees. The result should be 61º

Although it looks rather acute, f should be 95 degrees because it's a supplementary angle with 85º, meaning you subtract 85 from 180

The box in the triangle is just a symbol indicating a 90º angle