ngle ABC and angle CBD are complementary. The measure of angle ABC is \( 5 x+25 \). The measure of an CBD is \( x+5 \). Find the measure of angle ABC .

To find the measure of angle \( ABC \), let's analyze the given information: 1. **Complementary Angles:** \( \angle ABC \) and \( \angle CBD \) are complementary, which means their measures add up to \( 90^\circ \). 2. **Given Expressions:** - \( \angle ABC = 5x + 25 \) - \( \angle CBD = x + 5 \) 3. **Setting Up the Equation:** Since the angles are complementary: \[ (5x + 25) + (x + 5) = 90 \] 4. **Solving for \( x \):** \[ 5x + 25 + x + 5 = 90 6x + 30 = 90 6x = 60 x = 10 \] 5. **Finding \( \angle ABC \):** Substitute \( x = 10 \) into the expression for \( \angle ABC \): \[ \angle ABC = 5(10) + 25 = 50 + 25 = 75^\circ \] **Answer:** The measure of angle \( ABC \) is \( 75^\circ \).