Guided Practice

∠R≅∠Sangle r is congruent to angle s. If m∠R=3x+5m angle r equals 3 x plus 5 and m∠S=5x−25m angle s equals 5 x minus 25, solve for x and find m∠Rm angle r.

A.
75

B.
50

C.
35

D.
15

1 answer

Since \(\angle R \cong \angle S\), it means they have the same measure, so we can set up the equation:

\[ m\angle R = m\angle S \]

Given:
\[ m\angle R = 3x + 5 \]
\[ m\angle S = 5x - 25 \]

Set these two expressions equal to each other:
\[ 3x + 5 = 5x - 25 \]

To solve for \(x\), first subtract \(3x\) from both sides to simplify:
\[ 5 = 2x - 25 \]

Next, add 25 to both sides to isolate the term with \(x\):
\[ 30 = 2x \]

Finally, divide both sides by 2 to solve for \(x\):
\[ x = 15 \]

Now that we have \(x = 15\), we can find the measure of \(\angle R\) by substituting back into the expression for \(m\angle R\):
\[ m\angle R = 3x + 5 \]
\[ m\angle R = 3(15) + 5 \]
\[ m\angle R = 45 + 5 \]
\[ m\angle R = 50 \]

So, the measure of \(\angle R\) is 50.

The correct answer is:
B. 50