Think About the Process In ΔABC, m∠B is 5 times m∠A and m∠C is 20° less than 4 times m∠A. What equation is used to solve for the variable x? Find the measure of each angle.
Which of the following is the correct equation used to solve for the measure of each angle?
A. m∠A – m∠B – m∠C = 180°
B. m∠A – m∠B + m∠C = 180°
C. m∠A + m∠B + m∠C = 180°
D. m∠A + m∠B – m∠C = 180°
The correct equation to use is: C. m∠A + m∠B + m∠C = 180°.
Here’s a brief explanation: In any triangle, the sum of the angles is always 180°. Since you have angles A, B, and C in triangle ABC, you can express their measures in terms of each other and set up the equation as follows:
1. Let m∠A = x (this will be our variable).
2. Then, m∠B = 5x (since m∠B is 5 times m∠A).
3. And m∠C = 4x – 20° (since m∠C is 20° less than 4 times m∠A).
Now, substituting these expressions into the equation gives:
x + 5x + (4x – 20°) = 180°
This simplifies to 10x – 20° = 180°, leading to the solution for x.
Now you can find the measures of angles A, B, and C. If you need further help with that, feel free to ask!