Title: Triangle Angle Relationships in ΔABC

Question

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.)

Quizzma Team · Answer

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

Title: Triangle Angle Relationships in ΔABC

1 Answer