Answer: m∠3 = 30° and m∠8= 150° .
Step-by-step explanation:
From the given figure it can be seen that a and b are two parallel lines, where t is transversal intersecting them.
Also, m∠3=x, m∠8=5x
To find : m∠3, m∠8
Since ∠3=∠5 [Interior alternate angles]
So, m∠5 =m∠3= x
Also, ∠5+∠8=180° [Linear pair]
⇒ x + 5x = 180° [Substituted the value of ∠5 and ∠8 in terms of x ]
⇒ 6x = 180°
⇒ x = 30° [Divide both sides by 6]
That means,
m∠3 = 30°
and m∠8= 5(30° ) = 150°
Hence, m∠3 = 30° and m∠8= 150° .
