name the pair of angles in each figure of class 7 math try these
Answers
Chapter 5: Lines and Angles is all about different lines, line segments, and angles.
A line segment has two end points.
A ray has only one end point (its vertex).
A line has no end points on either side.
This chapter throws light on topics such as related angles, pair of lines. The chapter deals with different types of angles and lines. The types of angles discussed in this chapter are as follows:
Pairs of Angles Condition
Two complementary angles Measures add up to 90°
Two supplementary angles Measures add up to 180°
Two adjacent angles Have a common vertex and a common arm but no common interior
Linear pair Adjacent and supplementary
A linear pair is a pair of adjacent angles whose non-common sides are opposite rays.
All the types are discussed in detail and are supplemented with examples and short questions.
Under the topic pair of lines, various sub-sections are discussed namely:
Intersecting lines
Transversal
Angles made by a transversal
When two lines intersect (looking like the letter X) we have two pairs of opposite angles. They are called vertically opposite angles. They are equal in measure.
A transversal is a line that intersects two or more lines at distinct points.
Six angles discussed in this section:
1. Interior angles
2. Exterior angles
3. Pairs of Corresponding angles
4. Pairs of Alternate interior angles
5. Pairs of Alternate exterior angles
6. Pairs of interior angles on the same side of the transversal
Transversal of parallel lines
Subsequently the topic- Checking for Parallel Lines is also discussed in the chapter- Lines and Angles.
When a transversal cuts two lines, such that pairs of corresponding angles are equal, then the lines have to be parallel.
When a transversal cuts two lines, such that pairs of alternate interior angles are equal, the lines have to be parallel.
When a transversal cuts two lines, such that pairs of interior angles on the same side of the transversal are supplementary, the lines have to be parallel.
Several diagrams are also present in the chapter wherever required.
The chapter consists of a set of questions to test the basic understanding of the chapter followed by the summary of the discussion for quick recall.
Page No 101:
Question 1:
Find the complement of each of the following angles:
ANSWER:
The sum of the measures of complementary angles is 90º.
(i) 20°
Complement = 90° − 20°
= 70°
(ii) 63°
Complement = 90° − 63°
= 27°
(iii) 57°
Complement = 90° − 57°
= 33°
Page No 102:
Question 2:
Find the supplement of each of the following angles:
ANSWER:
The sum of the measures of supplementary anglesis 180º.
(i) 105°
Supplement = 180° − 105°
= 75°
(ii) 87°
Supplement = 180° − 87°
= 93°
(iii) 154°
Supplement = 180° − 154°
= 26°
Page No 102:
Question 3:
Identify which of the following pairs of angles are complementary and which are supplementary.
(i) 65°, 115° (ii) 63°, 27°
(iii) 112°, 68° (iv) 130°, 50°
(v) 45°, 45° (vi) 80°, 10°
ANSWER:
The sum of the measures of complementary angles is 90º and that of supplementary anglesis 180º.
(i) 65°, 115°
Sum of the measures of these angles = 65º + 115º = 180°
∴ These angles are supplementary angles.
(ii) 63°, 27°
Sum of the measures of these angles = 63º + 27º = 90°
∴ These angles are complementary angles.
(iii) 112°, 68°
Sum of the measures of these angles = 112º + 68º = 180°
∴ These angles are supplementary angles.
(iv) 130°, 50°
Sum of the measures of these angles = 130º + 50º = 180°
∴ These angles are supplementary angles.
(v) 45°, 45°
Sum of the measures of these angles = 45º + 45º = 90°
∴ These angles are complementary angles.
(vi) 80°, 10°
Sum of the measures of these angles = 80º + 10º = 90°
∴ These angles are complementary angles.
Page No 102:
Question 4:
Find the angle which is equal to its complement.
ANSWER:
Let the angle be x.
Complement of this angle is also x.
The sum of the measures of a complementary angle pair is 90º.
∴ x + x = 90°
2x = 90°