Chapter 11 Exam

A guide says an angle of 47° is obtuse. Explain the error and give the correct class.

The assigned question is: “A guide says an angle of 47° is obtuse. Explain the error and give the correct class.” A learner wrote: “I classified or constructed the angle of 47 degrees without measuring from the aligned zero ray; I reported obtuse.” Identify a concrete invalid step or assumption. Work out the correct result and explain why it is valid.

On a protractor a pair of adjacent angles measures 60° and 120°. Are they complementary or supplementary?

The assigned question is: “On a protractor a pair of adjacent angles measures 60° and 120°. Are they complementary or supplementary?” A learner wrote: “60 + 120 = 181. I used this intermediate value to finish the assigned problem.” Identify a concrete invalid step or assumption. Work out the correct result and explain why it is valid.

Two contractors propose triangles (19, 19, 19) and (19, 21, 23) cm. Which is equilateral?

The assigned question is: “Two contractors propose triangles (19, 19, 19) and (19, 21, 23) cm. Which is equilateral?” A learner wrote: “I ignored whether the given side lengths containing 19 satisfy the triangle inequality, and wrote The first (20, 19, 19).” Identify a concrete invalid step or assumption. Work out the correct result and explain why it is valid.

The corner labels of a triangular sign show 63° and 72°. Find the remaining angle and classify the triangle as acute or otherwise.

The assigned question is: “The corner labels of a triangular sign show 63° and 72°. Find the remaining angle and classify the triangle as acute or otherwise.” A learner wrote: “I used 360 degrees as the triangle angle total instead of 180 degrees, so I wrote 46°; acute.” Identify a concrete invalid step or assumption. Work out the correct result and explain why it is valid.

A diagram states that the exterior angle is 103° while its remote interiors are 51° and 42°. Explain the inconsistency.

The assigned question is: “A diagram states that the exterior angle is 103° while its remote interiors are 51° and 42°. Explain the inconsistency.” A learner wrote: “I used the adjacent interior angle rather than the exterior angle when considering 103 degrees, yielding It should be 94°.” Identify a concrete invalid step or assumption. Work out the correct result and explain why it is valid.

A proposed square has all four equal sides but contains a 70° angle. Is that sufficient for a square?

The assigned question is: “A proposed square has all four equal sides but contains a 70° angle. Is that sufficient for a square?” A learner wrote: “The proposed figure has equal sides and a 70° corner, so I marked it as a square.” Identify a concrete invalid step or assumption. Work out the correct result and explain why it is valid.

A designer splits a quadrilateral along a diagonal. Explain how that proves its angle sum, then find the fourth angle after 98°, 100°, 55°.

The assigned question is: “A designer splits a quadrilateral along a diagonal. Explain how that proves its angle sum, then find the fourth angle after 98°, 100°, 55°.” A learner wrote: “I used a total of 180 degrees for the four interior angles rather than 360 degrees, producing 361°; fourth 107°.” Identify a concrete invalid step or assumption. Work out the correct result and explain why it is valid.

A parallelogram has acute angle 79°. List its four corner measures.

The assigned question is: “A parallelogram has acute angle 79°. List its four corner measures.” A learner wrote: “I used the opposite-angle rule for a specified adjacent angle of 79 degrees and wrote 80°, 101°, 79°, 101°.” Identify a concrete invalid step or assumption. Work out the correct result and explain why it is valid.

Construct a parallelogram with sides 28 cm and 25 cm and a 60° included angle; state how to check opposing sides.

The assigned question is: “Construct a parallelogram with sides 28 cm and 25 cm and a 60° included angle; state how to check opposing sides.” A learner wrote: “I constructed the shape using the stated length 28 but did not enforce the named angle or parallel-side condition; my construction meets the answer Parallelogram with side lengths 29, 25 cm and 60° angle.” Identify a concrete invalid step or assumption. Work out the correct result and explain why it is valid.