Questions: If m angle B is two more than three times the measure of angle C, and angle B and angle C are complementary angles, find each angle measure.

Transcript text: If $m \angle B$ is two more than three times the measure of $\angle C$, and $\angle B$ and $\angle C$ are complementary angles, find each angle measure.

Solution

Solution Steps

Step 1: Define the Relationships Between the Angles

Given that $ m \angle B $ is two more than three times the measure of $ \angle C $, we can write the equation: \[ B = 3C + 2 \]

Step 2: Set Up the Complementary Angle Equation

Since $ \angle B $ and $ \angle C $ are complementary angles, their measures add up to $ 90^\circ $. Therefore, we have: \[ B + C = 90 \]

Step 3: Solve the System of Equations

We now have the following system of linear equations: \[ B = 3C + 2 \] \[ B + C = 90 \]

Substituting $ B $ from the first equation into the second equation: \[ (3C + 2) + C = 90 \] \[ 4C + 2 = 90 \] \[ 4C = 88 \] \[ C = 22 \]

Now, substituting $ C = 22 $ back into the first equation: \[ B = 3(22) + 2 \] \[ B = 66 + 2 \] \[ B = 68 \]

Final Answer

$\boxed{C = 22, B = 68}$

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!