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 the given angle expressions: \(2x + 3x + 4x = 180\).

Step2: Solve for \(x\)

Combine like terms: \(9x = 180\).
Divide both sides by 9: \(x = \frac{180}{9} = 20\).

Step3: Calculate each angle

• \(m\angle A = 2x = 2\times20 = 40^\circ\)
• \(m\angle B = 3x = 3\times20 = 60^\circ\)
• \(m\angle C = 4x = 4\times20 = 80^\circ\)

Step4: Evaluate each option

• Option 1: \(m\angle A = 20^\circ\) is false (it's \(40^\circ\)).
• Option 2: \(m\angle B = 60^\circ\) is true (calculated as \(60^\circ\)).
• Option 3: \(m\angle A + m\angle B = 40 + 60 = 100^\circ

eq 90^\circ\), so not complementary.

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

eq 100^\circ\), false.

Answer:

B. \(m\angle B = 60^\circ\)