Question

If the complement of the angle a is B and the supplement of the angle B is 4a, then find the measure of the angle B

Answer 1

`\alpha + \beta = 90`

`\beta + 4 \alpha = 180`

Multiply the upper system by -1:

`- \alpha - \beta = - 90`

`\beta + 4 \alpha = 180`

Add the systems:

`3 \alpha = 90`

`\alpha = 30`

`\beta = 90 - \alpha = 90 - 30 = 60`

`( \alpha = 30) < = > ( \beta = 60)`