Question

triangle abc has the angle measures shown.
m∠a = (2x)°
m∠b = (3x)°
m∠c = (4x)°
which statement is true about the angles?
○ m∠a = 20°
○ m∠b = 60°
○ ∠a and ∠b are complementary
○ m∠a + m∠c = 100°

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \(m\angle A + m\angle B + m\angle C = 180^\circ\). Substitute \(m\angle A=(2x)^\circ\), \(m\angle B=(3x)^\circ\), \(m\angle C=(4x)^\circ\):
\(2x + 3x + 4x = 180\)
\(9x = 180\)
\(x = 20\).

Step2: Calculate each angle

• \(m\angle A = 2x = 2(20) = 40^\circ\)
• \(m\angle B = 3x = 3(20) = 60^\circ\)
• \(m\angle C = 4x = 4(20) = 80^\circ\)

Step3: Evaluate each option

• Option 1: \(m\angle A = 20^\circ\)? No, \(m\angle A = 40^\circ\).
• Option 2: \(m\angle B = 60^\circ\)? Yes, from Step 2.
• Option 3: Are \(\angle A\) and \(\angle B\) complementary? Complementary angles sum to \(90^\circ\). \(40 + 60 = 100

eq 90\), so no.

• Option 4: \(m\angle A + m\angle C = 100^\circ\)? \(40 + 80 = 120

eq 100\), so no.

Answer:

B. \(m\angle B = 60^\circ\) (assuming the second option is labeled B; adjust identifier based on original options, but the correct statement is \(m\angle B = 60^\circ\))