Question

in the figure below, m∠1 = 3x° and m∠2=(x + 18)°. find the angle measures. m∠1 = (square^{circ}) m∠2=(square^{circ})

Explanation:

Step1: Use angle - sum property

Since the two angles ∠1 and ∠2 form a right - angle, m∠1 + m∠2=90°. Given m∠1 = 3x° and m∠2=(x + 18)°, we have the equation 3x+(x + 18)=90.

Step2: Simplify the left - hand side of the equation

Combine like terms: 3x+x+18 = 90, which simplifies to 4x+18 = 90.

Step3: Solve for x

Subtract 18 from both sides: 4x=90 - 18, so 4x=72. Then divide both sides by 4: x = 18.

Step4: Find m∠1

Substitute x = 18 into the expression for m∠1. m∠1=3x, so m∠1=3×18 = 54°.

Step5: Find m∠2

Substitute x = 18 into the expression for m∠2. m∠2=x + 18, so m∠2=18+18 = 36°.

Answer:

m∠1 = 54°
m∠2 = 36°