Question

Look at the figure and the conditional statement based on it.
If angle AXO is 23° and angle BXO is 44°, then angle AOB is 134°.

Samantha wrote a two column proof as shown.

Answer 1

Which statement describes the error she made in the proof?
Answer

She made an error in statement 5. Measure of angle XOA = 90° + 44° = 134°.

She made an error in statement 5. Measure of angle XOB = (180°– 2 x 44°) = 92°.

She wrote an incorrect reason for statement 5. She should have written the sum of the base angles of an isosceles triangle is 90°.

She wrote an incorrect reason for statement 6. She should have written the sum of linear pair of angles is 180°.

Answer 2

Statement

Reason
1.

Measure of angle AXO = 23°
Measure of angle BXO = 44°

Given
2.

Segment AO is congruent to segment XO.
Segment BO is congruent to segment XO.

Radii of the same circle are equal.
3.

Triangle AOX is isosceles.
Triangle BOX is isosceles.

If two sides of a triangle are congruent, then the triangle is isosceles.
4.

Measure of angle XAO = 23°
Measure of angle XBO = 44°

The base angles of an isosceles triangle are congruent.
5.

Measure of angle XOA = (180°– 2 x 23°) = 134°
Measure of angle XOB = 2 x 23° + 44° = 90°

The sum of the interior angles of a triangle is 180°.
6.

Let measure of angle AOB be w°
Then w + 134 + 92 = 360

The sum of angles around a point is 360°.
7.

w = 360 – 226 = 134
Therefore measure of angle AOB is 134°.

Subtraction property of equality.