Question

A student uses the vertical angles theorem and the definition of complementary angles to conclude m p t r equals 50 in the figure what mistake did the student make

The student use the definition for complementary angles instead of the definition of right angles
The student use the definition of complementary angles instead of the definition of vertical angles
The student used to definition of complementary angles instead of the definition of supplementary angles
The student use the definition of vertical angles instead of the definition of right angles​

Answer 1

The correct option is;

The student used the definition for complementary angles instead of the definition for supplementary angles

Explanation:

From the diagram, we have;

x + 28 = 2·x + 16 Reason vertically opposite angles are congruent

Therefore, we have;

28 = 2·x - x + 16

28 - 16 = 2·x - x = x

12° = x

x = 12°

From which we have;

∠QTP = (x + 28)° = (12 + 28)° = 40°

∠QTP = 40°

∠QTP and ∠PTR are angles at the point, T on the same side of the straight line segment QR

∴ ∠QTP and ∠PTR are supplementary angles; The sum of angles on a straight line = 180°

Therefore, ∠QTP + ∠PTR = 180°

Which gives;

40° + ∠PTR = 180°

∠PTR = 180° - 40° = 140°

∠PTR = 140°.

The difference between the obtained value of PTR and the value in question is given as follows 140° - 50° = 90°

Therefore, the error in the student solution is the use of the definition of complementary angles (two angles that have a sum 90°) instead of the definition of supplementary angles (two angles that have a sum 180°).