In the verge of coronavirus pandemic, we are providing FREE access to our entire Online Curriculum to ensure Learning Doesn't STOP!

# Ex.5.1 Q12 Lines and Angles - NCERT Maths Class 7

Go back to  'Ex.5.1'

## Question

Find the values of the angles $$x, y$$ and $$z$$ in each of the following:

Video Solution
Lines & Angles
Ex 5.1 | Question 12

## Text Solution

(i) Reasoning

There are two operations done in sequence. First, if one angle is $$55^\circ$$ then the angle opposite to it will also be $$55^\circ$$as vertically opposite angles are equal.

Also sum of $$\angle x + \angle y = 180^\circ$$ and $$\angle z + 55^\circ = 180^\circ.$$ Now, $$\angle x,\angle y$$ and $$\angle z$$ can be easily calculated.

Steps:

Solve for $$\angle x,\angle y$$ and $$\angle z:$$

(i) $$\angle x = 55^\circ$$ (Vertically opposite angle)

\begin{align} \angle x + \angle y &= 180^\circ \rm (Linear \,pair) \\55 ^\circ+ \angle y &= 180^\circ\\ \angle y &= 180^\circ- 55 ^\circ\\ \angle y &= 125 ^\circ\end{align}

Therefore$$\angle y= \angle z = 125^\circ$$ (Vertically opposite angle)

Hence, $$\angle x = 55^\circ,\angle y= 125^\circ,\angle z = 125^\circ$$

(ii) Reasoning

By using angle sum property find the value of $$x$$ and then find the value of $$y$$ and $$z.$$ Since the sum of $$y + z = 180^\circ.$$ Now, it’s a matter of finding $$y$$ and $$z.$$

By using angle sum property,

\begin{align}40^\circ \!+ \!x \!+ \!25^\circ &= 180^\circ \\ \text{(Angles on } &\text{straight line)}\\x + 65^\circ &= 180^\circ\\ x &= 180^\circ - 65^\circ = 115^\circ\end{align}

Also,

\begin{align}40^\circ + y &= 180^\circ\text{(Linear pair)}\\ y &= 180^\circ - 40^\circ\\ y &= 140^\circ\\y + z &= 180^\circ \text{(Linear pair)}\\140^\circ + z &= 180^\circ (y = 140^\circ)\\ z &= 180^\circ- 140^\circ\\ z &= 40^\circ \end{align}

Thus, $$x = 115^\circ,y = 140^\circ {\text {and}} \,\,z = 40^\circ$$

Learn from the best math teachers and top your exams

• Live one on one classroom and doubt clearing
• Practice worksheets in and after class for conceptual clarity
• Personalized curriculum to keep up with school