Question
https://quizizz.com/join/game/U2FsdGVkX1\%252BeMvCiMeR5NKGeciQ\%2528YetcCM IYQCVnScLIAt ItxicQ0au\%252FEFZrI9iAqH7nP7yDih 14/35 Angle ABC and angle CBD are complementary. The measure of angle ABC is \( 5 x+25 \). The measure of ang CBD is \( x+5 \). Find the measure of angle \( A B C \).
Ask by Huff Joseph. in the United States
Jan 25,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The measure of angle \( ABC \) is \( 75^\circ \).
Solution
To find the measure of angle \( ABC \), let's follow these steps:
1. **Understand the Relationship:**
Angles \( ABC \) and \( CBD \) are **complementary**, which means their measures add up to \( 90^\circ \).
2. **Set Up the Equation:**
Given:
- Measure of \( ABC = 5x + 25 \)
- Measure of \( CBD = x + 5 \)
Since they are complementary:
\[
(5x + 25) + (x + 5) = 90
\]
3. **Solve for \( x \):**
\[
5x + 25 + x + 5 = 90
\]
\[
6x + 30 = 90
\]
\[
6x = 90 - 30
\]
\[
6x = 60
\]
\[
x = \frac{60}{6} = 10
\]
4. **Find the Measure of Angle \( ABC \):**
\[
ABC = 5x + 25 = 5(10) + 25 = 50 + 25 = 75^\circ
\]
**Answer:**
The measure of angle \( ABC \) is **75 degrees**.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To find the measure of angle \( ABC \), we start by using the fact that complementary angles add up to \( 90^\circ \). Therefore, we can set up the equation: \[ (5x + 25) + (x + 5) = 90 \] Combining like terms gives: \[ 6x + 30 = 90 \] Now, subtract \( 30 \) from both sides: \[ 6x = 60 \] Dividing by \( 6 \) results in: \[ x = 10 \] Now, we can substitute \( x \) back into the expression for angle \( ABC \): \[ AB = 5(10) + 25 = 50 + 25 = 75 \] Thus, the measure of angle \( ABC \) is \( 75^\circ \).
