Question

The sum of the measures of the angles in any triangle is 180 degrees. In triangle ABC, angles A and B have the same measure, while angle C is 99 degrees larger than each of the other two angles. Find the measure of angle C.

A) 27 degrees
B) 153 degrees
C) 54 degrees
D) 126 degrees

Answer 1

The measure of angle C in triangle ABC, given that it is 99 degrees larger than the equal angles A and B, is calculated using the property that the sum of the angles in a triangle is 180 degrees. The result is that angle C measures 126 degrees.

Step-by-step explanation:

Calculating Angle Measures in a Triangle

The problem presented involves understanding the fundamental property of triangles, where the sum of the angles in a triangle is always 180 degrees. Given that triangle ABC has angles A and B of equal measure and angle C is 99 degrees larger than each of A and B, we can set up an equation to find the measure of angle C. Let's denote the measure of angles A and B as 'x'. Then, angle C can be represented as 'x + 99 degrees'. The sum of the angles can be expressed as:

x + x + (x + 99 degrees) = 180 degrees

Combining like terms gives us:

3x + 99 degrees = 180 degrees

Subtracting 99 degrees from both sides of the equation yields:

3x = 81 degrees

Dividing both sides by 3, we find that:

x = 27 degrees

Now that we know the measure of angles A and B, we can find angle C by adding 99 degrees to x:

Angle C = x + 99 degrees = 27 degrees + 99 degrees = 126 degrees

Therefore, the correct answer is D) 126 degrees.