Question

mathematical connections identify an algebraic equation you can use to find the measure of each ang description. then find the measure of each angle. the measure of an angle is 12° more than twice the measure of its complement. ○ x + (2x + 12) = 180 ○ x + (x + 12) = 90 ○ x + (2x + 12) = 90 ○ x + (2x - 12) = 90 the measure of the smaller angle is □°. the measure of the larger angle is □°.

Explanation:

Step1: Define Variables and Relationship

Let the measure of the complement angle be \( x \). The angle is \( 12^\circ \) more than twice its complement, so the angle is \( 2x + 12 \). Complementary angles sum to \( 90^\circ \), so the equation is \( x + (2x + 12) = 90 \).

Step2: Solve the Equation

Combine like terms: \( 3x + 12 = 90 \). Subtract 12: \( 3x = 78 \). Divide by 3: \( x = 26 \).

Step3: Find the Larger Angle

Substitute \( x = 26 \) into \( 2x + 12 \): \( 2(26) + 12 = 52 + 12 = 64 \).

Answer:

The correct equation is \( x + (2x + 12) = 90 \).
The measure of the smaller angle is \( 26^\circ \).
The measure of the larger angle is \( 64^\circ \).