Question

The measures of two supplementary angles are in the ratio 1:3. What is the measure, in degrees, of the larger angle?

Answer 1

Sum of two angles that are supplementary = 180°

Ratios in which they have been given their measurement = 1 : 3

Total number of parts = 1 + 3 = 4

Each part = 180÷4 =

$Each \: part = \: \frac{180}{4}$

Each part = 45°

Measure of smaller angle = 45 × 1 = 45°

$Measure \: of \ \: the \: smaller \: angle \: = \: 45 \: × \: 1 \: = \: 45°$

$Measure \: of \: \: the \: larger \: angle \: = \: 3 \: × \: 45 \: = \: 145° \:$

∴ The measure of the larger angle in degrees = 145° .