Question

In the diagram of ABC, line segment AC is extended to D. If mBCD = 140, and mABC = 85, what is the measure of angle BCD?

A) 45°
B) 55°
C) 95°
D) 140°

Answer 1

The measure of angle BCD is 95 degrees, as it is part of a linear pair with angle ABC, which measures 85 degrees, totaling 180 degrees for a straight line.

Step-by-step explanation:

To find the measure of angle BCD, we will rely on the fact that angle ABC and angle BCD are adjacent, forming a linear pair. Since a straight line is 180 degrees, we can add the measure of angle ABC (which is given as 85 degrees) to the measure of angle BCD and set this sum equal to 180 degrees:

mABC + mBCD = 180 degrees

85 + mBCD = 180 degrees

Solving for mBCD, we subtract 85 from both sides:

mBCD = 180 - 85

mBCD = 95 degrees

Hence, the correct answer is C) 95°.