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.

A triangle ABC is shown. The base of the triangle extends into a straight line. The angle formed between this straight line and the edge of the triangle is marked as w. The angle adjacent to w is marked as z, and the other two angles inside the triangle are marked as x and y.

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)
pls help me if you have Flvs

Answer 1

A.Step 1:
`m\angle x+ m\angle y+m\angle z=180^(\circ)`( Sum of angles of a triangle).

Explanation:

We are given that a triangle ABC. The base of triangle extends into a straight line .The angle formed between this straight line and the edge of the triangle is marked as w.

Then we can say w is exterior angle.

The angle z is adjacent to the exterior angle w.

The other two angle of triangle are x and y are given .

Step 1:
`m\angle x+m\angle y+m\angle z=180^(\circ)`

Reason: Sum of angles of triangle.

Step2:
`m\angle w+m\angle z=180^(\circ)`

Reason: supplementary angles.

Step 3: Therefore,
`m\angle x+m\angle y+m\angle z=m\angle w+m\angle z`.

Reason : Substitute two equations equal.

Step 4:So
`m\angle x+m\angle y=m\angle w`

Reason: Cancel both side
`m\angle z`.

Hence proved.

Therefore, the student first make a mistake in first step

Correct step 1 :
`m\angle x+m\angle y+m\angle z=180^(\circ)`

Reason : Sum of angles of a triangle.

Answer 2

Step 1; it should be m∠x + m∠y + m∠z = 180 degrees (sum of angles of a triangle)

Explanation:

The answer is self-explanatory. The sum of interior angles of a triangle is 180°.