Question

Find the size of the each of the angle marked with the letter in the diagram. Equal sides are marked by the dashes and parallel sides are marked by double arrows.

Answer 1

Step 1 : Use angle sum property of quadrilateral

Since sum of angles of quadrilateral is $360°$

$$\begin{gathered} \Rightarrow \angle a+\angle a+35°+67°=360° \\ \Rightarrow 2\angle a+102°=360° \\ \Rightarrow 2\angle a=360°-102° \\ \Rightarrow 2\angle a=258° \\ \therefore \angle a=129° \end{gathered}$$

Now,

$\angle a+\angle b=180°$ (It is linear pair)

$$\begin{gathered} \Rightarrow \angle b={180}^{\circ }-\angle a \\ \Rightarrow \angle b=180°-129°[\text{put the value of}\angle a] \\ \Rightarrow \angle b=51° \end{gathered}$$

Step 2 : Use angle sum property of triangle

Sum of all angles of triangle$=180°$

$$\begin{gathered} \Rightarrow {35}^{\circ }+\angle a+\angle c={180}^{\circ } \\ \Rightarrow 35°+129°+\angle c=180° \\ \Rightarrow \angle c=180°-164° \\ \therefore \angle c=16° \end{gathered}$$

Hence, the required value of angles are $\angle a=129°,\angle b=51°\text{and}\angle c=16°$