Think About the Process In ΔABC, m∠B is 4 times m∠A and m∠C is 20° less than 5 times m∠A. What equation is used to solve for the variable x? Find 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 measure of angle A is 20°.
(Simplify your answer. Type an integer or a decimal.)
The measure of angle B is 80°.
(Simplify your answer. Type an integer or a decimal.)
The measure of angle C is __°.
(Simplify your answer. Type an integer or a decimal.)
To solve the problem, we start by defining the measures of angles based on the given relationships:
1. Let ( m∠A = x ).
2. Since ( m∠B ) is 4 times ( m∠A ), we have ( m∠B = 4x ).
3. ( m∠C ) is 20° less than 5 times ( m∠A ), so ( m∠C = 5x – 20° ).
Now, according to the angle sum property of triangles, the sum of all angles in a triangle is 180°. Therefore, the correct equation is:
D. ( m∠A + m∠B + m∠C = 180° )
Substituting the expressions we found:
[
x + 4x + (5x – 20) = 180
]
Combining like terms gives:
[
10x – 20 = 180
]
Now, solving for ( x ), we add 20 to both sides:
[
10x = 200
]
Dividing by 10:
[
x = 20°
]
Now we can find the measures of each angle:
– ( m∠A = x = 20° )
– ( m∠B = 4x = 4(20) = 80° )
– ( m∠C