A right angle is formed by two adjacent angles with measures of (x)°

Question

and (x+30)°
. What are the two angle measures?(1 point)
Responses

60°
and 90°
60 degrees and 90 degrees

70°
and 25°
70 degrees and 25 degrees

30°
and 60°
30 degrees and 60 degrees

75°
and 105°

Answer 1

Two angles are said to form a right angle if their measures add up to 90 degrees. In this case, the adjacent angles are \(x\) degrees and \(x + 30\) degrees.

We can set up the equation:

\[ x + (x + 30) = 90 \]

Simplifying the equation:

\[ 2x + 30 = 90 \]

Subtracting 30 from both sides gives:

\[ 2x = 60 \]

Dividing by 2:

\[ x = 30 \]

Now, substituting \(x\) back into the expressions for the angles, we get:

1. First angle: \(x = 30°\)
2. Second angle: \(x + 30 = 30 + 30 = 60°\)

Thus, the two angles are \(30°\) and \(60°\).

So the correct response is:

30° and 60°.