Question

In the given figure, if $AB\parallel CD$ and $AC\parallel DE$, then find $\angle a + \angle b$.

A) ${70^ \circ }$
B) ${120^ \circ }$
C) $100^\circ $
D) $115^\circ $

Answer 1

Hint: Here since we have two sets of parallel lines, we can find the relation between the forming angles. When a transversal cuts two parallel angles the alternate angle formed will be equal. We can use this concept here. Also we know the angle around a point is $360^\circ $.

Formula used:
If we have two parallel lines and a transversal cuts these lines, the alternate interior angles formed will be equal in measurement.
Angle around a point is always ${360^ \circ }$.

Complete step-by-step answer:
Given that $AB\parallel CD$ and $AC\parallel DE$.
We have to find $\angle a + \angle b$.
Here since $AB\parallel CD$ and $AC$ is a line that intersects them, the pair of angles $a$ and $\angle ACD$ are alternate interiors.
If we have two parallel lines and a transversal cuts these lines, the alternate interior angles formed will be equal in measurement.
This gives $\angle ACD = a$
Also since $AC\parallel DE$ and $CD$ is a line intersecting them, the pair of angles $b$ and $\angle ACD$ are alternate interior.
If we have two parallel lines and a transversal cuts these lines, the alternate interior angles formed will be equal in measurement.
This gives $\angle ACD = b$
We know that angle around a point is always ${360^ \circ }$.
So, $\angle ACD = 360^\circ - 325^\circ = 35^\circ $
Therefore, we have, $a = 35^\circ ,b = 35^\circ $
We are asked to find $a + b$.
Substituting we get,
$a + b = 35^\circ + 35^\circ = 70^\circ $
$\therefore $ The answer is option A.

Note: We can do this question in another way too. Since $AB\parallel CD$ and $AC\parallel DE$, angles $a$ and $b$ are formed in between these lines gives $a = b$. So instead of finding both we only need to find one angle.