Question

Triangle ABC has the angle measures shown. begin mathsize 14px style m angle A space equals space left parenthesis 2 x right parenthesis degree m angle B space equals space left parenthesis 5 x right parenthesis degree m angle C space equals space left parenthesis 11 x right parenthesis degree end style Which statement is true about the angles? A. begin mathsize 14px style m angle A space equals space 20 degree end style B. begin mathsize 14px style m angle B space equals space 60 degree end style C. begin mathsize 14px style angle A space and space angle B end style are complementary D. begin mathsize 14px style m angle A space plus space m angle C space equals space 120 degree end style

Answer 1

Using the fact that the sum of all angles in a triangle is 180 degrees, we determine that x = 10. Then we calculate that angle A = 20 degrees, making statement A the correct answer A. begin mathsize 14px style m angle A space equals space 20 degree.

Step-by-step explanation:

To find out which statement is true about the angles of triangle ABC, we use the fact that the sum of angles in any triangle is 180 degrees. We have angle A = (2x) degrees, angle B = (5x) degrees, and angle C = (11x) degrees. Setting up the equation 2x + 5x + 11x = 180 gives us 18x = 180, which means x = 10.

Now, we can evaluate each option:

A. m angle A = 20 degrees is true because angle

A = 2x

= 2(10) = 20 degrees.

B. m angle B = 60 degrees is false because angle

B = 5x

= 5(10)

= 50 degrees, not 60 degrees.

C. angle A and angle B are complementary is false because angle A + angle B = 20 degrees + 50 degrees

= 70 degrees, and complementary angles add up to 90 degrees.

D. m angle A + m angle C = 120 degrees is false because m angle

A = 20 degrees and

m angle C = 11x

= 11(10) = 110 degrees,

so their sum is 130 degrees, not 120 degrees.

Therefore, the correct statement about the angles is A. m angle A = 20 degrees.