Question

in the figure, m∠1 = (x + 51)° and m∠2 = (2x)°. (a) write an equation to find x. make sure you use an \=\ sign in your answer. equation: \boxed{} (b) find the degree measure of each angle. m∠1 = \boxed{}° m∠2 = \boxed{}°

Explanation:

Part (a)

Step1: Identify angle relationship

The two angles form a right angle (90°), so their sum is 90°.

Step2: Write the equation

\( (x + 51) + 2x = 90 \)

Step1: Solve for \( x \)

Combine like terms: \( 3x + 51 = 90 \)
Subtract 51: \( 3x = 90 - 51 = 39 \)
Divide by 3: \( x = \frac{39}{3} = 13 \)

Step2: Find \( m\angle 1 \)

Substitute \( x = 13 \) into \( (x + 51) \): \( 13 + 51 = 64 \)

Step3: Find \( m\angle 2 \)

Substitute \( x = 13 \) into \( 2x \): \( 2 \times 13 = 26 \)

Answer:

\( (x + 51) + 2x = 90 \)

Part (b)