Question

Type the correct answer in the box. in triangle abc, which side is the longest if these are the measures of the angles? m?a = 60�, m?b = (3x ? 2)�, m?c = (2x 7)�

Answer 1

By solving for x using the sum of triangles' angles, we find that the largest angle in triangle ABC is angle B, meaning the opposite side, side AC, is the longest.

Step-by-step explanation:

In a triangle, the side opposite the largest angle is the longest. Given the angle measures in triangle ABC where m∠A = 60°, m∠B = (3x − 2)°, and m∠C = (2x + 7)°, we can first find the values of x by knowing the sum of the angles in a triangle equals 180°.

m∠A + m∠B + m∠C = 180°
60° + (3x − 2)° + (2x + 7)° = 180°
Combine like terms:
5x + 65 = 180°
Subtract 65 from both sides:
5x = 115
Divide by 5:
x = 23

Now substitute the value of x back into the expressions for angles B and C:
m∠B = (3(23) − 2)° = 67°
m∠C = (2(23) + 7)° = 53°.

Since the largest angle is B (67°), the side opposite to it, side AC, is the longest side in triangle ABC.

Answer 2

To find the longest side in triangle ABC, solve for x to determine the angles and then use the fact that the side opposite the largest angle is the longest. Angle B is the largest, therefore side AC is the longest.

Step-by-step explanation:

In triangle ABC, where the angles are given as m°A = 60°, m°B = (3x - 2)°, and m°C = (2x + 7)°, we can determine the longest side by first finding the values for x and then the measures of the angles B and C. According to the properties of triangles, the sum of the angles in a triangle is 180°. Therefore, we have:

60 + (3x - 2) + (2x + 7) = 180

5x + 65 = 180

5x = 115

x = 23

Now, substituting x back into the expressions for angles B and C:

m°B = (3x - 2)° = (3(23) - 2)° = 67°

m°C = (2x + 7)° = (2(23) + 7)° = 53°

Since angle B is the largest, side AC (opposite of angle B) will be the longest side in triangle ABC.