Question

In the figure given below, L ll M, then the value of x is:-

a) 30°
b) 45°
c) 50°
d) 60°

Answer 1

Hint: Before solving this question, one must be familiar to some of following explained terms:-
PARALLEL LINES: Two lines are said to be parallel if they do not meet, no matter how much they are extended in either direction.
TRANSVERSAL LINE: When a line cuts two or more parallel or non-parallel lines, that line is called a transversal line.

Complete step-by-step answer:
Given: L ll M
To Find: Value of x
 (3y)° = (2y + 25)° (Alternate interior angles are equal)
Therefore, y = 25°
(x + 15)° = (2y +25)°
\[\left( x+15 \right){}^\circ =\left( 2\times 25+25 \right){}^\circ \] (Vertically opposite angles are equal)
x = (75 – 15)°
x = 60°

OR

 (x +15)° = (3y)° (Corresponding Angles are equal)
\[~\left( x+15 \right){}^\circ =\left( 3\times 25 \right){}^\circ \]
x = (75 – 15)°
x = 60°
Hence, the value of x is (d) 60°.

Finding all the angles:-
(x + 15)° = (60 +15)° = 75°
\[\begin{array}{*{35}{l}}
   \left( 2y+25 \right){}^\circ =\left( 2\times 25+25 \right){}^\circ =\left( 50\text{ }+25 \right){}^\circ =75{}^\circ \\
   \left( 3y \right){}^\circ =\left( 3\times 25 \right){}^\circ =75{}^\circ \\
\end{array}\]

Note: When two parallel lines are cut by transversal lines:
1. Alternate exterior angles are equal.
2. Alternate interior angles are equal.
3. Corresponding angles are equal.
4. Co-interior angles are supplementary.
5. Exterior angles are supplementary.

In the figure given above, ‘m’ ll ‘n’ and ‘t’ is the transversal

a) Alternate exterior angles are:-
i. ∠1 and ∠8
ii. ∠2 and ∠7

b) Alternate interior angles are:-
i. ∠3 and ∠6
ii. ∠4 and ∠5

c) Corresponding angles are:-
i. ∠1 and ∠5
ii. ∠2 and ∠6
iii. ∠3 and ∠7
iv. ∠4 and ∠8

d) Co-interior angles are:-
i. ∠3 and ∠5
ii. ∠4 and ∠6

e) Exterior angles are:-
i. ∠1 and ∠2
ii. ∠7 and ∠8