Question

The diagram shows parallel lines cut by two transversal lines creating a triangle. Which statements are true? Check all that apply.

m∠A = 20°
∠B and the angle marked 60° are alternate exterior angles.
m∠C = 100° because it is a vertical angle to the angle marked 100°.
∠B and ∠C are supplementary angles.
m∠A + m∠B + m∠C = 180°

Answer 1

A
C
E

Explanation:

Answer 2

`m<A = 20\°`

`m<C = 100\°`

`m<A+m<B+m<C < 180\°`

Explanation:

Verify each statement

case A)
`m<A = 20\°`

The statement is True

we know that

The measure of angle A is equal to the angle marked
`20\°` by corresponding angles

case B) ∠B and the angle marked
`60\°` are alternate exterior angles

The statement is False

Because, ∠B and the angle marked
`60\°` are corresponding angles

case C)
`m<C = 100\°` because it is a vertical angle to the angle marked
`100\°`

The statement is True

we know that

`m<C = 100\°` ------> by vertical angles

case D) ∠B and ∠C are supplementary angles

The statement is False

we know that

`m<B+m<C < 180\°` ---> the sum is less than
`180\°`

case E)
`m<A+m<B+m<C < 180\°`

The statement is True

we know that

`m<A+100\°+m<B = 180\°`

and remember that

`m<C = 100\°`

so

substitute

`m<A+m<B+m<C < 180\°`