Question

in the figure, m∠1 = (x + 18)° and m∠2 = (3x)°. (a) write an equation to find x. make sure you use an \=\ sign in your answer. equation: box (b) find the degree measure of each angle. m∠1 = box °, m∠2 = box °.

Explanation:

Part (a)

Step1: Identify angle relationship

From the figure, \( \angle 1 \) and \( \angle 2 \) form a right angle, so their sum is \( 90^\circ \).
Thus, the equation is \( (x + 18) + 3x = 90 \).

Step2: Simplify the equation

Combine like terms: \( x + 3x + 18 = 90 \) ⟹ \( 4x + 18 = 90 \).

Step1: Solve for \( x \)

Subtract 18 from both sides: \( 4x = 90 - 18 = 72 \).
Divide by 4: \( x = \frac{72}{4} = 18 \).

Step2: Find \( m\angle 1 \)

Substitute \( x = 18 \) into \( m\angle 1 = (x + 18)^\circ \):
\( m\angle 1 = 18 + 18 = 36^\circ \).

Step3: Find \( m\angle 2 \)

Substitute \( x = 18 \) into \( m\angle 2 = 3x^\circ \):
\( m\angle 2 = 3 \times 18 = 54^\circ \).

Answer:

(Equation):
\( 4x + 18 = 90 \)

Part (b)