Solve Equations with Adjacent Angles Quick Check

Question

3 of 53 of 5 Items
Question
A right angle is formed by two adjacent angles with measures of (x)°
and (x+30)°
. What are the two angle measures?(1 point)
Responses

60°
and 90°
60 degrees and 90 degrees

30°
and 60°
30 degrees and 60 degrees

70°
and 25°
70 degrees and 25 degrees

75°
and 105°
75 degrees and 105 degrees
Skip to navigation
page 12 of 12

Answer 1

To solve for the measures of the two adjacent angles that form a right angle, we start with the information provided in the problem.

We have:

• One angle is \( x \) degrees
• The other angle is \( x + 30 \) degrees
• Together, these angles form a right angle, which measures \( 90 \) degrees.

This gives us the equation: \[ x + (x + 30) = 90 \]

Now, we can simplify and solve for \( x \): \[ 2x + 30 = 90 \] Subtract \( 30 \) from both sides: \[ 2x = 60 \] Now divide by \( 2 \): \[ x = 30 \]

Now that we have \( x \), we can find the measures of both angles:

1. The first angle is \( x = 30^\circ \).
2. The second angle is \( x + 30 = 30 + 30 = 60^\circ \).

Thus, the two angle measures are: 30° and 60°

The correct response is: 30° and 60°.