In triangle ABC, if m<A is seven more than four times m<B and m<C is eleven more than m<B, find the measure of <A.

Answer 1

to simplify, let angle A = <A = A, angle B = <B = B, and angle C = <C = C

this is a 3 equations in 3 unknowns problem

equation 1:

A = 7 + 4*B

equation 2:

C = 11 + B

equation 3: we know from geometry the total measure of the 3 angles of a triangle is 180 degree

A + B + C = 180

Now from equation 3, C = 180 - A - B

use this value for C and substitute in equation 2, then: 180 - A - B = 11 + B, which is A = 169 - 2B

use this value for A and substitute in equation 1, then: 169 - 2B = 7 + 4B, which is 6B = 162

if 6B = 162, then B = 162/6 = 27 degrees

use the value of B and substitute in equations 1 and 2, you will get

equation 1:

A = 7 + 4B = 7 + (4*27) = 115 degrees

equation 2:

C = 11 + B = 11 + 27 = 38 degrees

Answer 2

if m<A is: m<A =

seven more than: m<A = 7+

four times m<B: m<A = 7 + 4 * m<B

and m<C is: m<C =

eleven more than m<B: m<C = 11 + m<B

We have one more hidden equation: ABC is a triangle, so sum of internal angles is 180: m<A+m<B+m<C=180

A = 7 + 4B

C = 11 + B

A + B + C = 180

Substitute first and second equations in the third one:

(7+4B) + B + (11+B) = 180

6B + 18 = 180 (divide both sides by 6)

B + 3 = 30

B = 27

A = 7 + 4B = 7 + 108 = 115

C = 11 + B = 11 + 27 = 38