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

Answer 1

Step 1; it should be m∠m + m∠n + m∠o = 180 degrees (sum of angles in a triangle)

Step 2; it should be m∠o + m∠p = 180 degrees (alternate exterior angles)

Explanation:

The question is incomplete. Find the complete question in the comment section and the diagram attached

Since sum of angle in a triangle is 180° and the angles in the triangle shown are <m, <n and <o, therefore the student first step should be;

<m + <n + <o = 180°...... 1 (sum if angle in a triangle is 180°

Also <o and <p lies on a straight line. This two angle are the alternate exterior angles and the sum of the angles is 180° since the sum of angle on a straight line is 180°. Hence the step two should be;

<o+<p = 180° ....... 2(alternate exterior angle)

Substituting equation 2 into 1, equation 1 will become;

<m + <n + <o = <o+<p (Step 3)

Step 4:

Subtract <o from both sides to get the final expression.

<m + <n + <o - <o= <o+<p -<o

<m + <n = <p

Hence the correct step for 1 and 2 according to the solution are;

Step 1; it should be m∠m + m∠n + m∠o = 180 degrees (sum of angles in a triangle)

Step 2; it should be m∠o + m∠p = 180 degrees (alternate exterior angles)