Question

1) angle 1 and angle 2 are supplementary angles. If m 21 = (4x )° and m 22 = (8x), then find themeasures of these angles.

Answer 1

We know that

• Angle 1 and 2 are supplementary.

,

• Angle 1 is equal to 4x, and angle 2 is equal to 8x.

Rember that supplementary angles are those which sum 180°,

$m\angle1+m\angle2=180$

Replacing all given expressions, we have

$4x+8x=180$

Now, we solve for x

$\begin{gathered} 12x=180 \\ \frac{12x}{12}=\frac{180}{12} \\ x=15 \end{gathered}$

With this value, we can find each angle.

$\begin{gathered} m\angle1=4x=4\cdot15=60 \\ m\angle2=8x=8\cdot15=120 \end{gathered}$

Therefore, the angles are 60° and 120°.