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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 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∠o = 180 degrees (sum of angles of a triangle) Step 2: m∠p − m∠o = 90 degrees (alternate interior angles) Step 3: Therefore, m∠m + m∠n + m∠o = m∠o + m∠p Step 4: So, m∠m + m∠n = m∠p In which step did the student first make a mistake and how can it be corrected?

Respuesta :

should it be m>m+m>n+mo for first step

The exterior angle p is outside the triangle therefore, it cannot form one of the angles in the triangle.

What is the angle sum property?

The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.

In the triangle, let the exterior angle be p.

The adjacent interior angle = 0

The two opposite angles are marked m and n

m∠m + m∠n + m∠p = 180 degrees (sum of angles of a triangle)

m∠p + m∠o = 180 degrees (adjacent supplementary angles)

Therefore, m∠m + m∠n + m∠o = m∠o + m∠p

So, m∠m + m∠n = m∠p

m∠m + m∠n + m∠o = 180 degrees (sum of angles in a triangle).

So, p is outside the triangle therefore, it cannot form one of the angles in the triangle.

Learn more about the triangles;

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