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Karo-lina-s [1.5K]
3 years ago
14

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.
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 p. The angle adjacent to p is marked as o, and the other two angles inside the triangle are marked as m and n.

Step 1: m∠m + m∠n + m∠p = 180 degrees (sum of angles of a triangle)
Step 2: m∠p + m∠o = 180 degrees (adjacent supplementary angles)
Step 3: Therefore, m∠m + m∠n + m∠o = m∠o + m∠p
Step 4: So, m∠m + m∠n = m∠p

Please help, must be correct! In which step did the student first make a mistake and how can it be corrected?

Step 1; it should be m∠m + m∠n + m∠o = 180 degrees (sum of angles in a triangle)
Step 1; it should be m∠m + m∠n + m∠o = 90 degrees (adjacent angles)
Step 2; it should be m∠o + m∠p = 180 degrees (alternate exterior angles)
Step 2; m∠p − m∠o = 90 degrees (alternate interior angles)
Mathematics
1 answer:
mihalych1998 [28]3 years ago
5 0

Answer: The first option

Step-by-step explanation:

I'm smart

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Image provided below.

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3 years ago
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Step-by-step explanation:

Pythagoras' theorem for the smallest one :

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Using the formula before (for b^2) it becomes :

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Verifying :

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