Question

Which statement is true about the angles?

Triangle ABC has the angle measures shown

ZA=(2x)"

m2 =(5x)"

MLA=20

m2 = 60

ZA and 2 are complementary

LA+ m2 = 220°

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Answer 1

Measure of angle A = 20 degrees

Explanation:

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Answer 2

Complete Question:

Triangle abc has the angle mesausres shown.

m<A = (2x)°

m<B = (5x)°

m<C = (11x)°

Which statement is true about the angles?

A. m<A = 20°

B. m<B = 60°

C. m<A and m<B are complementary

D. m<A + m<C = 120°

Answer:

A. m<A = 20°

Explanation:

m<A + m<B + m<C = 180° (sum of interior angles of a triangle)

`2x + 5x + 11x = 180` (substitution)

Solve for x. Add like terms.

`18x = 180`

Divide both sides by 18

`(18x)/(18) = (180)/(18)`

`x = 10`

Find the measure of each angle by substituting x = 10:

m<A = (2x)° = 2(10) = 20°

m<B = (5x)° = 5(10) = 50°

m<C = (11x)° = 11(10) = 110°

Therefore, the only true statement is:

A. m<A = 20°