Question

in the figure, m∠1 = (5x)° 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: Use the property of complementary angles

Since \(\angle1\) and \(\angle2\) are complementary (they form a right - angle), we know that \(m\angle1 + m\angle2=90^{\circ}\). Given \(m\angle1=(5x)^{\circ}\) and \(m\angle2=(x + 6)^{\circ}\), the equation is \(5x+(x + 6)=90\).

Step2: Solve the equation for \(x\)

Combine like terms: \(5x+x+6 = 90\), which simplifies to \(6x+6=90\).
Subtract 6 from both sides: \(6x+6 - 6=90 - 6\), so \(6x=84\).
Divide both sides by 6: \(x=\frac{84}{6}=14\).

Step3: Find \(m\angle1\)

Substitute \(x = 14\) into \(m\angle1=(5x)^{\circ}\). Then \(m\angle1=5\times14 = 70^{\circ}\).

Step4: Find \(m\angle2\)

Substitute \(x = 14\) into \(m\angle2=(x + 6)^{\circ}\). Then \(m\angle2=14 + 6=20^{\circ}\).

Answer:

(a) Equation: \(5x+(x + 6)=90\)
(b) \(m\angle1 = 70^{\circ}\), \(m\angle2=20^{\circ}\)