Question

In figure, $$AB||CD$$ and $$\angle 1$$ and $$\angle 2$$ are in the ratio $$3:2$$. Determine all angles from $$1$$ to $$8$$.

Answer 1

As per diagram $$ AB||CD$$

and we know that sum of angles in a straight line is $$180^o$$

let the unknown angle be $$x$$

$$\angle 1:\angle 2= 3x : 2x$$

$$\angle 1+\angle 2=180^o$$

$$ 3x+2x=180^o$$

$$5x=180^o$$

$$x=36^o$$

=> $$\angle 1 = 3 \times 36^o=108^o$$

=> $$\angle 2 = 2 \times 36^o=72^o$$

We know that vertically opposite angles are equal.

$$\angle 1=\angle 3= 108^o$$

$$\angle 2=\angle 4= 71^o$$

We know that corresponding angles are equal.

$$\angle 1=\angle 5= 108^o$$

$$\angle 2=\angle 6= 71^o$$

$$\angle 4=\angle 8= 71^o$$

$$\angle 3=\angle 7= 108^o$$

$$\therefore$$ $$\angle 1=\angle 5=\angle 3=\angle 7= 108^o$$ and

$$\angle 2=\angle 6 = \angle 4=\angle 8= 71^o$$