Page 158 - NUMINO Challenge_B2

2 Square AEFG is formed by folding square CEFD; 4A

therefore, they have the same shape and size. FG
Therefore, the measures of angles FEC and FEA
are each 72 . The measure of angle AEB is D 60 E
180 (72 72 ) 36 . In triangle ABE, angle
ABE is a right angle; therefore, the measure of BC
angle BAE is 180 (36 90 ) 54 .
In triangle ADE, since the measure of angles DAE
3 and AED are each 60 , the measure of angle
40 ADE is also 60 . Also, in right triangle DEF, the
70 measure of angle FDE is 180 (90 60 ) 30 .
40 Therefore, since the measures of the unfolded
50 angle and folded angle are equal, the measure of
the colored angle is (60 30 ) 2 15 .
50

When you unfold the folded part, angle

overlaps with angle 70 ; therefore, it also

measures 70 . In 70 180 , since

70 70 180 , 180 140 40 . When

you draw a line that is parallel to the two

horizontal sides of the square and use the fact

that the measures of the corresponding angle

and the alternate angle are equal, then the

measure of angle is 50 .

Answer Key