# Ex.6.3 Q3 Lines and Angles Solution - NCERT Maths Class 9

## Question

In Fig. below, if \(AB || DE\), \(\angle BAC = 35^\circ \) and \(\angle CDE = 53^\circ \), find \(\angle DCE\).

## Text Solution

**What is known?**

\(AB || DE\), \(\angle BAC = 35^\circ \) and \(\angle CDE = 53^\circ \)

**What is unknown?**

\(\angle DCE\)

**Reasoning:**

As we know when two parallel lines are cut by a transversal, alternate interior angles formed are equal.

Angle sum property of a triangle:

Sum of the interior angles of a triangle is \(360^\circ\).

**Steps:**

Given,

\(AB || DE\) , \(\angle BAC = 35^\circ \) and \(\angle CDE = 53^\circ \)

\(\begin{align}\angle DEC &= \!\angle BAC\\( \text{Alternate }&\text{interior angles})\\\\\angle DEC &= 35^\circ \end{align}\)

Now, in \(\Delta CDE\)

\(\begin{align}\angle CDE + \angle DEC + \angle DCE &= 180^\circ\quad \\( \text{Angle sum property of a}&\text{ triangle.})\\\\53^\circ + 35^\circ + \angle DCE &= 180^\circ \\\angle DCE &\!= 180^\circ \! - 88^\circ \\\angle DCE &= 92^\circ\end{align}\)