Question

triangle abc has the angle measures shown. which statement is true about the angles?

m∠a=(2x)°
m∠b=(5x)°
m∠c=(11x)°

○ m∠a=20°
○ m∠b=60°
○ ∠a and ∠b are complementary
○ m∠a + m∠c=120°

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 measures: \((2x)^\circ + (5x)^\circ + (11x)^\circ = 180^\circ\).

Step2: Solve for \(x\)

Combine like terms: \(18x = 180\).
Divide both sides by 18: \(x = 10\).

Step3: Find each angle measure

• \(m\angle A = 2x = 2\times10 = 20^\circ\)
• \(m\angle B = 5x = 5\times10 = 50^\circ\)
• \(m\angle C = 11x = 11\times10 = 110^\circ\)

Step4: Evaluate each option

• Option 1: \(m\angle A = 20^\circ\) (matches our calculation, check others to be sure)
• Option 2: \(m\angle B = 50^\circ

eq 60^\circ\) (false)

• Option 3: \(m\angle A + m\angle B = 20 + 50 = 70^\circ

eq 90^\circ\) (not complementary, false)

• Option 4: \(m\angle A + m\angle C = 20 + 110 = 130^\circ

eq 120^\circ\) (false)

Answer:

\(m\angle A = 20^\circ\) (the first option: \(m\angle A = 20^\circ\))