Question

What are the measures of Angles a, b, and c? Show your work and explain your answers. (10 points)

Two straight lines intersect at a point to form an angle a. The measure of the angle opposite to angle a is 40 degrees. Angle a is the angle of a right triangle having another angle equal to b. A triangle with one angle labeled c is on the left of the figure. The angle adjacent to c is labeled 65 degrees.

Answer 1

Find the angles a, b and c from the given problem.

Explanation:

• Two straight lines intersecting at one point makes four angles, two acute angles, and two obtuse angles.
• These two pairs of acute and obtuse angles make two pairs, one of the adjacent angles having sum $180$ and the other of opposite angles which are equal.
• hence from the problem we have, $\angle a=40$  
• now a and b are angles from a right triangle hence,  $\angle a+\angle\ b=90\ \ \ \ ->\angle\ b=50$  
• now angle c is adjacent to the given angle hence, $\angle\ c+65=180\ \ \ \ \ ->\angle\ c=115$  
• Measures of angles a, b and c are $40,\ 50, \ and\ 115$ degrees respectively.