Question

Classify △ABC by its angles if m∠A=x, m∠B=2x, and m∠C=3x.

a) Right
b) Obtuse
c) Equilateral
d) Isosceles

Answer 1

Triangle ABC is a right triangle with angle A measuring 30 degrees, angle B measuring 60 degrees, and angle C measuring 90 degrees.

Step-by-step explanation:

To classify Triangle ABC by its angles, we need to consider the measures of angles A, B, and C, which are represented by x, 2x, and 3x respectively.

If the sum of the measures of the angles in a triangle is 180 degrees, then we can set up an equation:

x + 2x + 3x = 180

6x = 180

x = 30

Now, we can substitute x back into the angle measures to find their actual values:

Angle A = 30 degrees

Angle B = 2(30) = 60 degrees

Angle C = 3(30) = 90 degrees

Based on these angle measures, Triangle ABC is a right triangle, so the correct answer is (a) Right.