Question

A and B are complementary angles. If A = (x + 6) andB = (7x + 30) then find the measure of A

Answer 1

Concept:

Two angles are said to be complementary when they add up together to give 90 degrees

`\begin{gathered} \angle A+\angle B=90^0 \\ \text{where,} \\ \angle A=(x+6) \\ \angle B=(7x+30)^0 \end{gathered}`

By substituting the values, we will have

`\begin{gathered} \angle A+\angle B=90^0 \\ x+6+7x+30=90^0 \\ \text{collect similar terms, we will have} \\ x+7x+6+30=90 \\ 8x+36=90 \\ \text{substract 36 from both sides} \\ 8x+36-36=90-36 \\ 8x=54 \\ \text{divide both sides by 8} \\ (8x)/(8)=(54)/(8) \\ x=6.75 \end{gathered}`

To determine the value of angle A,

We will substitute the value of x= 6.75 below

`\begin{gathered} A=x+6 \\ A=6.75+6 \\ A=12.75^0 \end{gathered}`

Hence,

A= 12.75°