Question

In the adjoining figure. line p ll line q. line l ll line m. Find measures of

/a , /b , and /c, using the measures of given angles. Justify your answer​

Answer 1

Step-by-step explanation:

40

∘

+u=180

∘

⇒u=140

∘

ω+u=180

∘

⇒ω=180°−u

=40°

∠z=70°(vertically opposite angles)

∠y+∠z=180°

⇒∠y=180°−∠z

180°−70°

=110°

⇒ω+x=180

∘

∴x=140

∘

Answer 2

Answer:

Given:

Line p || line q and line l are transversal.

Line l || line m and line p is a transversal.

Line p || line q and line m is a transversal.

Firstly let us find the measure of ∠a

Line p || line q and line l are transversal.

So,

m∠a + 80° = 180° [Since, they are interior angles]

m∠a= 180° – 80°

m∠a= 100°

Now, line l || line m and line p is a transversal.

So, m∠c = 80° … (i) [By using exterior alternate angles]

Line p || line q and line m is a transversal.

So, m∠b = m∠c … [Since, they are corresponding angles]

m∠b = 80° … [From equation (i)]

∴ The measure of ∠a is 100°, m∠b is 80°, m∠c is 80°.