Question

Two supplementary angles measure \(5x + 15^\circ\) and \(4x - 6^\circ\), angle are

• A. \(120^\circ, 60^\circ\)
• B. \(95^\circ, 85^\circ\)
• C. \(100^\circ, 80^\circ\)
• D. \(110^\circ, 70^\circ\)

Hint:

For supplementary angles, their sum should always be 180°. Solve the equation accordingly.

Answer 1

The Correct Option is C

The angles are supplementary, so their sum is \(180^\circ\). The equation is: \[ (5x + 15) + (4x - 6) = 180 \] Simplification yields: \[ 9x + 9 = 180 \quad \Rightarrow \quad 9x = 171 \quad \Rightarrow \quad x = 19 \] Substitute \(x = 19\) to find the angles: \[ 5x + 15 = 5 \cdot 19 + 15 = 100^\circ, \quad 4x - 6 = 4 \cdot 19 - 6 = 80^\circ \] The answer is \(100^\circ, 80^\circ\).