Page 157 - NUMINO Challenge_B2
P. 157
Answer
Key
3 Angle Interior angle Angle 3 Angle GFH is formed by folding angle GFC;
108 36 72 . therefore, angle GFC is 50 . The sum of the
measure of angles GFH, GFC, and HFE is 180 ;
therefore, the measure of angle HFE is 180
(50 50 ) 80 .
4 In triangle HEF, the measures of the two angles
besides angle EHF are 60 and 80 , respectively.
Therefore, the measure of angle EHF is 180
(60 80 ) 40 .
Problem solving Problem solving
1 Since triangle EBC is an equilateral triangle, the 1 Angles FCE and DCE are equal; therefore, the
measure of angle BCE is 60 . Angles ECG and measure of each angle is (90 40 ) 2 25 .
DCG are the same; therefore, each angle Since the measure of angles EFC and EDC are
measures (90 60 ) 2 15 . Therefore, the each 90 , the measure of angles FEC and DEC
measure of angle CGD in the right triangle CDG are each 180 90 25 65 . Therefore, the
is 180 90 15 75 . measure of angle AEF is 180 (65 65 ) 50 .
2
The measure of angle is equal to the angle 2 Angle FHG is formed by folding angle GHC;
formed when a parallel line intersects with
another line. Therefore, the measure of angle therefore, the measure of angle GHC is 35 .
Angle EFH measures the same as angle FHC;
is 34 34 68 . therefore, it's 35 35 70 . Therefore, the
measure of angle is 70 because it is the
opposite angle of angle EFH and has the same
measure.
Creative Thinking p.82~p.83
Type 9-2 Folding Angles p.80~p.81 1
120
1 Since angle DEH is formed by folding angle
DEB, the measures of the 2 angles are the same.
Therefore, the measure of angle DEB is 60 .
2 The sum of angles DEH, DEB, and HEF is 180 . In a regular hexagon, the measure of an interior
Therefore, the measure of angle HEF is 180 angle is 120 . The folded triangle is an isosceles
triangle; therefore, the measure of angle is
(60 60 ) 60 . (180 120 ) 2 30 . The folded angle
measures the same as when it is unfolded;
therefore, the measure of angle is
120 (30 30 ) 60 .
NUMINO Challenge B2
Key
3 Angle Interior angle Angle 3 Angle GFH is formed by folding angle GFC;
108 36 72 . therefore, angle GFC is 50 . The sum of the
measure of angles GFH, GFC, and HFE is 180 ;
therefore, the measure of angle HFE is 180
(50 50 ) 80 .
4 In triangle HEF, the measures of the two angles
besides angle EHF are 60 and 80 , respectively.
Therefore, the measure of angle EHF is 180
(60 80 ) 40 .
Problem solving Problem solving
1 Since triangle EBC is an equilateral triangle, the 1 Angles FCE and DCE are equal; therefore, the
measure of angle BCE is 60 . Angles ECG and measure of each angle is (90 40 ) 2 25 .
DCG are the same; therefore, each angle Since the measure of angles EFC and EDC are
measures (90 60 ) 2 15 . Therefore, the each 90 , the measure of angles FEC and DEC
measure of angle CGD in the right triangle CDG are each 180 90 25 65 . Therefore, the
is 180 90 15 75 . measure of angle AEF is 180 (65 65 ) 50 .
2
The measure of angle is equal to the angle 2 Angle FHG is formed by folding angle GHC;
formed when a parallel line intersects with
another line. Therefore, the measure of angle therefore, the measure of angle GHC is 35 .
Angle EFH measures the same as angle FHC;
is 34 34 68 . therefore, it's 35 35 70 . Therefore, the
measure of angle is 70 because it is the
opposite angle of angle EFH and has the same
measure.
Creative Thinking p.82~p.83
Type 9-2 Folding Angles p.80~p.81 1
120
1 Since angle DEH is formed by folding angle
DEB, the measures of the 2 angles are the same.
Therefore, the measure of angle DEB is 60 .
2 The sum of angles DEH, DEB, and HEF is 180 . In a regular hexagon, the measure of an interior
Therefore, the measure of angle HEF is 180 angle is 120 . The folded triangle is an isosceles
triangle; therefore, the measure of angle is
(60 60 ) 60 . (180 120 ) 2 30 . The folded angle
measures the same as when it is unfolded;
therefore, the measure of angle is
120 (30 30 ) 60 .
NUMINO Challenge B2
