Question

Solve: The angles of a triangle are described as follows: ZA is the largest angle; its measure is three times the measure

of LB. The measure of ZC is 5 less than the measure of ZB. Find the measures of the three angles in degrees. Use
the following equation: x+3x+x-5= 180 (m/B = x)
(A) 18°, 54°, 13°
B36, 108°, 31°
37°, 111°, 32°
D) 58, 174, 53

Answer 1

To solve the problem, assign variables to the angles and set up an equation. Solve the equation to find the values of the angles. LB = 25 degrees, ZA = 75 degrees, ZC = 70 degrees.

Step-by-step explanation:

To solve this problem, let's assign variables to the angles. Let's say the measure of angle LB is x degrees. According to the problem, the measure of angle ZA is three times the measure of LB, so ZA is 3x degrees. The measure of angle ZC is 5 less than ZB, so ZC is (3x - 5) degrees.

We know that the sum of the angles in a triangle is 180 degrees. Therefore, we can set up the equation: x + 3x + (3x - 5) = 180. Simplifying this equation, we get 7x - 5 = 180. Solving for x, we find that x = 25.

Substituting this value back into the equations, we find that LB = 25 degrees, ZA = 3x = 75 degrees, and ZC = 3x - 5 = 70 degrees.

Learn more about Triangle angles