Question

If m∠F=5x+30,m∠G=3x+30 and the angles, ∠F and ∠G are supplementary, find the measures of the two angles.

Answer 1

GIVEN:

We are told that two angles F and G are supplementary angles.

The angle measures are as follows;

`\begin{gathered} \angle F=5x+30 \\ \\ \angle G=3x+30 \end{gathered}`

Required;

To find the measure of the two angles.

Step by step solution;

When two angles are identified as supplementary angles, it means they add up to 180 degrees. Therefore, for the angles F and G, we can set up the following equation;

`\begin{gathered} \angle F+\angle G=180 \\ \\ (5x+30)+(3x+30)=180 \\ \\ 5x+30+3x+30=180 \\ \\ Collect\text{ }like\text{ }terms: \\ \\ 5x+3x+30+30=180 \\ \\ 8x+60=180 \\ \\ Subtract\text{ }60\text{ }from\text{ }both\text{ }sides: \\ \\ 8x=120 \\ \\ Divide\text{ }both\text{ }sides\text{ }by\text{ }8: \\ \\ x=15 \end{gathered}`

The two angles therefore are as follows;

`\begin{gathered} \angle F=5x+30 \\ \\ \angle F=5(15)+30 \\ \\ \angle F=75+30 \\ \\ \angle F=105\degree \end{gathered}`
`\begin{gathered} \angle G=3x+30 \\ \\ \angle G=3(15)+30 \\ \\ \angle G=45+30 \\ \\ \angle G=75\degree \end{gathered}`

ANSWER

Angle F = 105 degrees

Angle G = 75 degrees