lines L parallel M and P parallel Q find a value of a,b,c and d
Answers
Answer:
a=120°
\angle \: b \: = 60 \degree∠b=60°
\angle \: c \: = 60 \degree \:∠c=60°
\angle \: d \: = 120 \degree∠d=120°
Step - by - step explanation
To find the angles first name them to know the names refer to attachment
given : \angle lrn \: = 60 \degree \:given:∠lrn=60°
l, m, n and p are parallel
To find : a, b, c and d
Solution
\angle \: a \: + 60 \degree \: = 180 \degree∠a+60°=180°
They both are corresponding angles
\implies \: \angle \: a \: = 180 \degree \: - 60 \degree⟹∠a=180°−60°
\implies \: \angle \: a = 120 \degree⟹∠a=120°
Now,
\angle \: d \: = \angle \: a∠d=∠a
Angle a and d are alt. exterior angle
\therefore \: \angle \: d \: = 120 \degree∴∠d=120°
Now,
\angle \: c \: + \angle \: d \: = 180 \degree∠c+∠d=180°
They both are linear pair
\angle \: c \: + 120 \degree \: = 180 \degree∠c+120°=180°
\implies \: \angle \: c \: = 180 \degree - 120 \degree⟹∠c=180°−120°
\implies \: \angle \: c \: = 60 \degree⟹∠c=60°
And
\angle \: b \: = \angle \: c∠b=∠c
They both are opposite angles
\therefore \: \angle \: b \: = 60 \degree∴∠b=60°