Download (2) (5) The student did not follow directions. The student put the

(2) (5) The student did not follow directions. The student put the three triangles
together instead of cutting out the 3 angles of each triangle and putting
them together. Had the student of done that they would have gotten
that the triangles do form an angle of 180 degrees. I woul give them no
more than one point
(6) The student has the wrong rule, but the rule that they wrote down is
correct based on their answer in Step 5. Because of this I would give
them 8 or 9 points.
(13) (a) The figure isn’t closed so it isn’t a triangle
(b) The figure has 4 sides instead of 3 so it isn’t a triangle
(c) The figure is closed and has 3 sides so it is a triangle
(17) (a) x + 25 + 75 = 180. So x + 100 = 180. Subtracting 100 from both sides
gives that x = 80. The triangle is an acute triangle because the angles
are all acute angles.
(b) x + 52 + 38 = 180. So x + 90 = 180. Subtracting 100 from both sides
gives that x = 90. The triangle is a right triangle because there is a right
angle.
(c) x + 48 + 38 = 180. So x + 86 = 180. Subtracting 86 from both sides gives
that x = 94. The triangle is an obuse triangle because there is an obtuse
angle.
(d) x + 44.6 + 59.1 = 180. So x + 103.7 = 180. Subtracting 103.7 from both
sides gives that x = 76.3. The triangle is an acute triangle because the
angles are all acute angles.
(23) (a) x + x + 36 = 180. So 2x + 36 = 180. Subtracting 36 from both sides gives
that 2x = 144. So x = 72 The triangle is an acute triangle because the
angles are all acute angles. The triangle is isoceles because two sides are
congruent.
(b) x + 32 + 116 = 180. So x + 148 = 180. Subtracting 100 from both sides
gives that x = 32. The triangle is an obtuse triangle because there is an
obtuse angle. The triangle is isoceles because two sides are congruent.
(c) x + 104 + 55 = 180. So x + 159 = 180. Subtracting 100 from both sides
gives that x = 21. The triangle is an obtuse triangle because there is an
obtuse angle. The triangle is scalene because no sides are congruent.
(d) x + x + x = 180. So 3x = 180. Hence x = 60. The triangle is an acute
triangle because the angles are all acute angles.
(26) It is not possible for an obtuse angle to be complimentary to another angle.
If it were so then the sum of the 2 angles would be 90 degrees, but an obtuse
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angle has measure greater than 90 , so it can’t have a measure of 90 degrees
when it is added to another angle.
(30) The student added the measure of the other 2 angles to 180, but they should
have subtracted the measures of the other angles from 180. The correct answer
should be x = 86. I would encourage the student to review the section on
finding angle measures.
(34) (a) This is never true. An obtuse angle has measure greater than 90 degrees,
so 2 obtuse angles would have measure greater than 180 degrees and
hence they aren’t supplementary.
(b) This is sometimes true. If one angle measures 30 degrees and the other
measures 60 degrees, then there sum is 90 and they are both complimentary and acute. On the other hand if one angle measures 30 degrees and
the other measures 70 degrees, then there sum is 100 and they are acute
but not complimentary.
(c) This is always true. Since the sum of the angles of a triangle measures
180 degrees, and the right angle measures 90 degrees, the remaining acute
angles must sum to 90 degrees.
(d) This is never true. If 2 angles were supplementary, then the measure of
there sum would be 180 degrees, but since the sum of the angles of the
triangle measure 180 degrees, this means that the third angle has measure
0 degrees. Every angle needs to have positive measure in a triangle, so
this can’t be true.