Question

Complete the statements to find the measurements of ∠a and ∠b. In a triangle with angles labeled 40 degrees and 35 degrees, find the measurement of angle ∠a. Then, a line extends from angle ∠a to form an exterior angle, which is labeled ∠b. Calculate the measurement of angle ∠b. A) ∠a = 85 degrees, ∠b = 95 degrees B) ∠a = 105 degrees, ∠b = 125 degrees C) ∠a = 75 degrees, ∠b = 85 degrees D) ∠a = 115 degrees, ∠b = 135 degrees

Answer 1

The measure of angle 'a' in the triangle is 105 degrees and exterior angle 'b' is 75 degrees.

Step-by-step explanation:

To find the measurements of angles ∠a and ∠b within a triangle with the other angles given as 40 degrees and 35 degrees, we should first understand that the sum of the internal angles of a triangle always equals 180 degrees. Therefore, we can calculate the measure of angle ∠a by subtracting the given angles from 180: 180 - 40 - 35 = 105 degrees. So, ∠a = 105 degrees.

Then, to find ∠b, which is an exterior angle of the triangle (the angle formed by one side of the triangle and the extension of an adjacent side), we should remember that an exterior angle equals the sum of the two opposite interior angles. Considering our triangle, these two angles are 40 degrees and 35 degrees. Therefore, ∠b = 40 + 35 = 75 degrees.

So the answer would be ∠a = 105 degrees, ∠b = 75 degrees.

Learn more about Triangle Angles