Please answer......
Answers
Answer :
★ Question 1
Fill in the blanks
❒ Solution :
a) Two adjacent angles are said to to form linear pair of the angles if their non-common terms are opposite rays.
b) If a ray stands on a line then the sum of the adjacent angles so formed is 180°
c) The sum of all angles around a point is 360°
d) An angle which is equal to it's complement is 45°
e) two angles are called a pair straight angle of if their arms from two pairs of opposite rays.
f) If two angles intersect then the vertically opposite angles are equal.
g) A line which intersects two or more lines at a distinct points is called a transversal.
h) You can draw infinite transversals on a line.
i) If two lines are intersected by a transversal such that any pair of corresponding angles are equal then the lines are parallel.
★ Question 2
Two parallel lines l is parallel to m are intersected by a transversal. If the interior angles on same side of transversal are ( 2x - 8 )° , ( 2x - 8 )° and ( 3x - 7 )° , ( 3x - 7 )°. Find the measure of these angles.
❒ Solution : -
We know that,
The interior angles of same sides are supplementary,
Therefore,
⟹ 2x - 8 + 3x - 7 = 180
⟹ 2x + 3x = 180 + 7 + 8
⟹ 5x = 195
⟹ x = 195 / 5
⟹ x = 39
Therefore, the angles are :-
•» 2x - 8
» 2 × 39 - 8
» 78 - 8
» 70°
•» 3x - 7
» 3 × 39 - 7
» 117 - 7
» 110°
Therefore, the angles are :- 70° and 110°
★ Question 3
Find the measure of a , b , c and d
❒ Solution :
∠ d = 100° ...... opposite angles are equal.
∠ b = 100° ...... alternate angle.
∠ c = 100° ....... corresponding angle.
To find ∠ a , we need to find out the interior angle first of ∠ d
= 180 - 100
= 80
∴ ∠ d interior angle = ∠a .... opposite angle
∠ a = 80°