Question

in the figure, m∠1=(7x)° and m∠2=(x - 6)°. (a) write an equation to find x. make sure you use an = sign in your answer. equation: (b) find the degree measure of each angle. m∠1=° m∠2=°

Explanation:

Step1: Identify angle - relationship

Since the two angles ∠1 and ∠2 are complementary (they form a right - angle), the sum of their measures is 90°. So the equation is \(m\angle1 + m\angle2=90\). Substituting \(m\angle1=(7x)^{\circ}\) and \(m\angle2=(x - 6)^{\circ}\), we get the equation \(7x+(x - 6)=90\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(7x+x-6 = 90\), which simplifies to \(8x-6 = 90\).

Step3: Solve for x

Add 6 to both sides of the equation: \(8x-6 + 6=90 + 6\), so \(8x=96\). Then divide both sides by 8: \(x=\frac{96}{8}=12\).

Step4: Find \(m\angle1\)

Substitute \(x = 12\) into the expression for \(m\angle1\): \(m\angle1=7x=7\times12 = 84^{\circ}\).

Step5: Find \(m\angle2\)

Substitute \(x = 12\) into the expression for \(m\angle2\): \(m\angle2=x - 6=12-6 = 6^{\circ}\).

Answer:

(a) Equation: \(7x+(x - 6)=90\)
(b) \(m\angle1 = 84^{\circ}\), \(m\angle2 = 6^{\circ}\)