Question

The sum of two opposite angles of a quadrilateral is \[{172^ \circ }\] . The other two angles of the quadrilateral are equal. Find the equal angles.

Answer 1

Hint: The sum of all internal angles of a quadrilateral is given by \[{360^ \circ }\] so use this property to find the sum of other two opposite angles and then divide by two to get the angles individually.

Complete step by step answer:
So we are given that the two opposite angles are \[{172^ \circ }\]
We also know that the sum of all interior angles of a triangle is \[{360^ \circ }\]
Now let us imagine the unknown angles be x
It is given that the rest of the two angles are equal, which means the sum of these will be
\[x + x = 2x\]
Now the value of 2x will be
\[\begin{array}{l}
\therefore {178^ \circ } + 2x = {360^ \circ }\\
 \Rightarrow 2x = {182^ \circ }\\
 \Rightarrow x = {91^ \circ }
\end{array}\]

Now it is clear that the angles are \[{91^ \circ }\] each.

Note: The sum of all interior angles of any closed shapes is always \[{360^ \circ }\] like for example if a shape is the regular hexagon which has 6 sides and 6 angles then we now that in a regular hexagon all angles are same then each angle will be of \[{60^ \circ }\] also note that in order of all angles to be the same ‘REGULAR’ term must be present along with the figure.