Questions: CONNECTING CONCEPTS The measure of an angle is 6° less than the measure of its complement. Identify and solve an algebraic equation. x+(x+6)=90 x+(x-6)=90 x+(x+6)=180 x+(x-6)=180 Find the measure of each angle.

Solution Steps

To solve the problem, we need to identify the correct algebraic equation that represents the relationship between the angle and its complement. The complement of an angle is defined as the angle that, when added to the original angle, equals $90^{\circ}$. We are given that the measure of the angle is $6^{\circ}$ less than its complement. Therefore, we need to solve the equation $x + (x + 6) = 90$.

1. Identify the correct equation: $x + (x + 6) = 90$.
2. Simplify and solve for $x$.
3. Calculate the measure of each angle.

We are given that the measure of an angle is \(6^\circ\) less than the measure of its complement. The complement of an angle \(x\) is \(90^\circ - x\). Therefore, the correct equation is: \[ x + (x + 6) = 90 \]

Simplify the equation: \[ x + x + 6 = 90 \] \[ 2x + 6 = 90 \] Subtract 6 from both sides: \[ 2x = 84 \] Divide by 2: \[ x = 42 \]

The measure of the first angle is: \[ x = 42^\circ \] The measure of the second angle, which is \(6^\circ\) more than the first angle, is: \[ x + 6 = 42 + 6 = 48^\circ \]

Final Answer