Question

A student writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle ABC below is equal to the measure of the exterior angle.

Step 1: m∠x + m∠y + m∠z = 90 degrees (sum of adjacent angles)
Step 2: m∠w + m∠z = 180 degrees (supplementary angles)
Step 3: Therefore, m∠x + m∠y + m∠z = m∠w + m∠z
Step 4: So, m∠x + m∠y = m∠w

In which step did the student first make a mistake and how can it be corrected?

Step 1; it should be m∠x + m∠y + m∠z = 180 degrees (sum of angles of a triangle)
Step 1; it should be m∠x + m∠y + m∠z = 180 degrees (corresponding angles)
Step 2; it should be m∠w + m∠z = 90 degrees (supplementary angles)
Step 2; it should be m∠w + m∠z = 90 degrees (adjacent angles)

Answer 1

The correct answer is A.  All triangles' interior angles equal 180.

Answer 2

The correct option is 1.

Explanation:

The according to the angle sum property of triangle, the sum of interior angles of a triangle is 180°.

Step 1: According to the student in triangle ABC,

`\angle x+\angle y+\angle z=90^(\circ)`

Which is not correct because the sum of interior angles of a triangle is 180°. So, he did a mistake in step 1.

In triangle ABC,

`\angle x+\angle y+\angle z=180^(\circ)` ... (1) (sum of angles of a triangle)

Step 2:
`\angle w+\angle z=180^(\circ)` .... (2) (supplementary angles)

Step 3: Equating (1) and (2), we get

`\angle x+\angle y+\angle z=\angle w+\angle z`

Stpe 4:
`\angle x+\angle y=\angle w`

Therefore the correct option is 1.