Page 156 - NUMINO Challenge_B2
P. 156
Problem solving 3 The measure of an interior angle in a regular
1 When you stretch the sides of the trapezoid that pentagon is 108 ; it is 60 in an equilateral
triangle and 90 in a square. Therefore, the
are not parallel to each other, you can make an measure of angle is 360 108 60 90
isosceles triangle as shown below. 102 .
Vertex 4 The measure of an angle of a regular pentagon is
Since the sum of the nine vertices in the equal to the sum of the interior angles of a
isosceles triangle is 360 , the measure of one pentagon divided by 5. Therefore, 180 3 540
vertex is 360 9 40 . The remaining two and 540 5 108 . Since the measure of both
angles have the same measure; therefore, the angle FAE and angle FEA is 180 108 72 ,
measure of angle is (180 40 ) 2 70 . the measure of angle AFE is 180 72 72 36 .
2 9 Folding and Angles p.76~p.77
Example EB, EC EC, equilateral triangle
Example
Creative Thinking p.74~p.75
1 The sum of all the marked angles is equal to the FEG FG, isosceles triangle
sum of the interior angles of the triangle and Type 9-1 Finding the Measure of Angles p.78~p.79
square. Therefore, 180 360 540 .
1 A pentagon can be divided into three triangles;
2 The shapes and have curved lines; therefore, the sum of the interior angles is 180
3 540 . Since there are five interior angles in
therefore, there will be gaps where the shapes a regular pentagon, the measure of one angle is
are connected. 540 5 108 .
In shape , the sum of three angles is 180 ;
therefore, when two of each of the three 2 The measure of an interior angle in a regular
different angles meet at a vertex, tessellation is pentagon is 108 , and in the colored triangle the
possible. measure of the two angles besides 108 are
In shape , the sum of the four angles is 360 ; equal. Therefore, the measure of angle is
therefore, when four different angles meet at a (180 108 ) 2 36 .
vertex, the tessellation is possible.
In shape , the measure of an angle is 135 .
Therefore, when two octagons are connected,
90 will be left and when three octagons are
connected, the shapes will overlap and
tessellation is not possible. Therefore,
tessellation is possible with and .
Answer Key
1 When you stretch the sides of the trapezoid that pentagon is 108 ; it is 60 in an equilateral
triangle and 90 in a square. Therefore, the
are not parallel to each other, you can make an measure of angle is 360 108 60 90
isosceles triangle as shown below. 102 .
Vertex 4 The measure of an angle of a regular pentagon is
Since the sum of the nine vertices in the equal to the sum of the interior angles of a
isosceles triangle is 360 , the measure of one pentagon divided by 5. Therefore, 180 3 540
vertex is 360 9 40 . The remaining two and 540 5 108 . Since the measure of both
angles have the same measure; therefore, the angle FAE and angle FEA is 180 108 72 ,
measure of angle is (180 40 ) 2 70 . the measure of angle AFE is 180 72 72 36 .
2 9 Folding and Angles p.76~p.77
Example EB, EC EC, equilateral triangle
Example
Creative Thinking p.74~p.75
1 The sum of all the marked angles is equal to the FEG FG, isosceles triangle
sum of the interior angles of the triangle and Type 9-1 Finding the Measure of Angles p.78~p.79
square. Therefore, 180 360 540 .
1 A pentagon can be divided into three triangles;
2 The shapes and have curved lines; therefore, the sum of the interior angles is 180
3 540 . Since there are five interior angles in
therefore, there will be gaps where the shapes a regular pentagon, the measure of one angle is
are connected. 540 5 108 .
In shape , the sum of three angles is 180 ;
therefore, when two of each of the three 2 The measure of an interior angle in a regular
different angles meet at a vertex, tessellation is pentagon is 108 , and in the colored triangle the
possible. measure of the two angles besides 108 are
In shape , the sum of the four angles is 360 ; equal. Therefore, the measure of angle is
therefore, when four different angles meet at a (180 108 ) 2 36 .
vertex, the tessellation is possible.
In shape , the measure of an angle is 135 .
Therefore, when two octagons are connected,
90 will be left and when three octagons are
connected, the shapes will overlap and
tessellation is not possible. Therefore,
tessellation is possible with and .
Answer Key
