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uysha [10]
3 years ago
8

A student writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle ABC b

elow 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)

Mathematics
2 answers:
lana [24]3 years ago
6 0

Answer:

The correct option is 1.

Step-by-step 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.

blsea [12.9K]3 years ago
5 0
The correct answer is A.  All triangles' interior angles equal 180.
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