Question

Angle A is complementary to Angle B, Angle B is supplementary to Angle C, and the ratio of Angle A to Angle C is 11:26. Find the measurements of Angle B.

Answer 1

Since the complementary angles have a sum of 90 degrees

Since

$A+B=90^{\circ}\rightarrow(1)$

Since the supplementary angles have a sum of 180 degrees

Since

$B+C=180^{\circ}\rightarrow(2)$

Subtract (1) from (2) to eliminate B

$\begin{gathered} (B-B)+(C-A)=(180-90) \\ C-A=90\rightarrow(3) \end{gathered}$

Since the ratio between A and C is 11: 26

Then the difference in ratio between C and A is

$\begin{gathered} C-A=26x-11x \\ C-A=15x\rightarrow(4) \end{gathered}$

Equate (3) and (4) to find x

$15x=90$

Divide both sides by 15

$\begin{gathered} \frac{15x}{15}=\frac{90}{15} \\ x=6 \end{gathered}$

Substitute x in the ratio of A and C to find them

$\begin{gathered} A=11x \\ A=11\times6 \\ A=66^{\circ} \end{gathered}$

Substitute it in equation (1) to find B

$66+B=90$

Subtract 66 from both sides

$\begin{gathered} 66-66+B=90-66 \\ B=24^{\circ} \end{gathered}$

Angle B is 24 degrees