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Solving 7th-grade math problems on pages 94 and 95, Chapter 1 of the Cánh Diều book with detailed solutions for exercises 1, 2, 3, 4 of the lesson Special Angle Positions. Refer for easier understanding and completing exercises. If unsure, review previous lesson materials.
Referencing multiple good study materials for 7th-grade Mathematics:
- Solving 7th-grade Math problems from the Cánh Diều book
- Solving 7th-grade Math problems on page 45, Chapter 1 of the Kết Nối Tri Thức book - Exercise 8: Special Angle Positions. Bisector of an angle
- Solving 7th-grade Math problems on page 72, Chapter 1 of the Chân Trời Sáng Tạo book - Exercise 1: Special Angles
Solving 7th-grade math problems on pages 94 and 95, Chapter 1 of the Cánh Diều book
Exercise 1. Special Angle Positions
1. Solve Exercise 1 Page 94 in Math Textbook for 7th Grade
Problem Statement: a) Find the pairs of adjacent angles in figures 18a, 18b.
b) Find the pairs of complementary angles in figure 19.
c) Find two vertex opposite angles (other than the obtuse angle) in each of figures 20a, 20b, 20c, 20d.
Solution Guide:
+ 2 angles sharing a vertex, sharing one side, and the remaining two sides lying on opposite sides of the line containing the shared side are adjacent angles.
+ 2 complementary angles are adjacent and together form a straight angle.
+ Two vertex opposite angles are two angles where each side of one angle is the opposite ray of a side of the other angle.
Answer:
a) Two adjacent angles:
In figure 18a: angle iAj and angle jAk.
In figure 18b: angle eBf and angle fBg; angle eBf and angle fBh; angle eBg and angle gBh; angle fBg and angle gBh.
b) Complementary angle pairs in Figure 19 are: angle xOy and angle yOu; angle xOz and angle zOu; angle xOt and angle tOu.
c) 2 vertex opposite angles:
In Figure 20a: None because these 2 angles do not share a vertex.
In Figure 20b: There isn't any because no two angles have each side of one angle as the opposite ray of a side of the other angle.
In Figure 20c: angles xOy and x'Oy'.
In Figure 20d: There isn't any because no two angles have each side of one angle as the opposite ray of a side of the other angle.
2. Solve Problem 2 Page 95 Math Textbook Grade 7
Problem: Observe Figure 21 and identify:
a) Two adjacent angles;
b) Two adjacent supplementary angles;
c) Two vertical angles.
Solution Guide:
+ Two angles with a common vertex, share one side, and the remaining two sides lie on opposite sides of the line containing the shared side are adjacent angles.
+ Two angles are supplementary if they are both adjacent and complementary to each other.
+ Vertical angles are two angles where each side of one angle forms a straight line with a side of the other angle.
Answers:
a) 2 adjacent angles are: angle ABE and EBD; angle AFG and GFE; angle AEB and BED; angle BCG and GCD; angle FGB and BGC; angle BGC and CGE; angle CGE and EGF; angle EGF and FGB.
b) 2 supplementary angles are: angle AFG and GFE; angle BCG and GCD; angle FGB and BGC; angle BGC and CGE; angle CGE and EGF; angle EGF and FGB.
c) 2 vertical angles are: angle FGB and CGE; angle BGC and EGF.
3. Solve Problem 3 Page 95 Math Textbook Grade 7
Problem: Find the measure of:
a) Angle mOp in Figure 22a;
b) Angle qPr in Figure 22b;
c) x, y in Figure 22c.
Solution Guide:
Answers:
4. Solve Problem 4 Page 95 Math Textbook Grade 7
Problem: Figure 23 is a sample of a door with a circular arch of a house. If we consider each door arch brace as a side of an angle, then these braces form adjacent angles. According to you, how many degrees is each angle formed by two door arch braces?
Solution Guide:
The sum of two supplementary angles is 180 degrees.
Answers:
There are 4 adjacent angles formed, arranged into a straight angle, each angle formed by 2 door arch braces. Therefore, each angle measures: 180° ÷ 4 = 45°.
Here, Mytour has guided Grade 7 Mathematics solving page 94, 95 Volume 1 of the Kite book exercise 1: Special position angles, you can preview the next lessons to prepare for knowledge.
- Solve Grade 7 Mathematics page 98, 99 Volume 1 Kite - Exercise 2. Angle bisector of an angle
- Solve Grade 7 Mathematics page 104 Volume 1 Kite - Exercise 3. Two parallel lines
