Question

what is the measure of the supplement?

Answer 1

The measure of the supplement is x = 6º

To solve this, we'll call the angle A. We know that the angle A is 29 times greater than x and two times larger than" means "three times as large as". This means that with 29 supplements we'd make 1 angle A.

In an expression, this would be:

$A=29x$

We also know that A and x are supplementary angles, therefore:

$x+A=180º$

With these two expressions, we can solve the system:

$\begin{gathered} \begin{cases}A=29x \\ x+A=180º\end{cases} \\ x+A=180º\Rightarrow A=180º-x \end{gathered}$

Now we replace A in the first equation:

$\begin{gathered} 180º-x=29x \\ 180º=29x+x \\ \\ 180º=30x \\ x=\frac{180º}{30} \\ x=6º \end{gathered}$

-------------------------------------------------------------------------------------------------------------------------------------------------------------------------Part 2:

Now to find the measure of the angle A, we know that they're supplementary. Then:

A + x = 180º

Since x = 6º:

A + 6º = 180º

A = 180º - 6º

A = 174º