Question

(d) problem 22: (first taught in lesson 16)
the measure of an angle is 6 greater than half the measure of its supplement. find the measure of the angle.
after you enter your answer press go.

Explanation:

Step1: Define the angle and its supplement

Let the angle be $x$. Its supplement is $180 - x$.

Step2: Set up the equation

The problem states that $x=\frac{1}{2}(180 - x)+6$.

Step3: Expand the right - hand side

$x = 90-\frac{1}{2}x+6$.

Step4: Combine like terms

$x+\frac{1}{2}x=90 + 6$.

Step5: Simplify the left - hand side

$\frac{2x+x}{2}=96$, so $\frac{3x}{2}=96$.

Step6: Solve for $x$

Multiply both sides by $\frac{2}{3}$: $x = 96\times\frac{2}{3}=64$.

Answer:

$64^{\circ}$