Question

PLEASE HELP BRO WILL GIVE BRAINLI

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 = 180 degrees (adjacent supplementary angles)
Step 3: Therefore, m∠m + m∠n + m∠o = m∠n + 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? (4 points)

Step 2; it should be m∠o − m∠p = 90 degrees (complementary angles)
Step 1; it should be m∠m + m∠n + m∠o = 90 degrees (adjacent angles)
Step 1; it should be m∠m + m∠n + m∠o = 90 degrees (corresponding angles)
Step 3; it should be m∠m + m∠n + m∠o = m∠o + m∠p

Answer 1

Step 3; it should be angle m + angle n + angle o = angle o + angle p

Explanation:

yes, the sum of the inner angles of the triangle, m, n, o must be 180°.

yes, the sum of supplementary angles (which the pair of inner and outer angles always is) p and o must be 180°.

so, step 3 wants to show that the sum of the 3 inner angles is the same as the sum of the inner/outer angle pair. m + n + o = o + p = 180.

but instead of o the student suddenly wrote n in the right side of the equation. and that is wrong. n + p can't be 180°, as both are inner angles, and that would make the third inner angle 0°, which is not really possible.

so, once n is replaced by o on the right side of the equating in step 3, all is correct again.

and step 4 is correct anyway (it fixed the mistake in step 3 of the original proof by another mistake, coming to the right conclusion just by coincidence), now that step 3 is corrected.