Question

In the adjoining figure, it is given that $\angle A=60$, $CE\parallel BA$ and $\angle ECD=65$. Then $\angle ACB$ equal to:
A. 60

B. 55
C. 70
D. 90

Answer 1

Hint: First we are going to draw the diagram and then we will use some properties of the triangle to find the required angle as if there is a straight line then the sum of all the angles on the line will be equal to 180.

Complete step by step answer:
First we will look at the definition of alternate angles,
Alternate angle: One of a pair of angles with different vertices and on opposite sides of a transversal at its intersection with two other lines one of a pair of angles inside the two intersected lines.
Let’s first draw the figure,

We can see that $CE\parallel BA$and $\angle A=60$,
Hence $\angle ECA$ and $\angle A$ are alternate angles hence these two must be equal as per given in the diagram.
Now we can see that $\angle BCD$ = 180, as it is a straight line.
Hence,
$\angle BCD=\angle ECD+\angle ECA+\angle ACB$
Now substituting the values of all the given values of the angles we get,
180 = 65 + 60 +$\angle ACB$
$\angle ACB$ = 180 – 125
$\angle ACB$ = 55
Hence the correct option will be (b).

Note: Here we use the fact that a straight line makes a 180 degree angle, one can also solve this question by taking the given triangle and then using the fact that the sum of all angles of a triangle is 180, the answer that we will get will be the same.