Question

Find the value of $$x$$ in the following figure.

Answer 1

Hint:To solve this question we have to use the concept which tells that if we start from one place and return to that same place on a circular boundary then the covered angle is $${360}^{\circ }$$. From there we are able to find all the unknown angles if they have the same variable. We add all the angles given in the figure and equation all of them to $${360}^{\circ }$$.

Complete step by step answer:
Given, a fig is given in which angles are given.

$$\mathrm{\angle }AOB={47}^{\circ }$$
$$\Rightarrow \mathrm{\angle }COD={83}^{\circ }$$
$$\Rightarrow \mathrm{\angle }AOB={92}^{\circ }$$
$$\Rightarrow \mathrm{\angle }AOB={75}^{\circ }$$
To find the unknown angle which is given in the angle.
$$\mathrm{\angle }BOC=x^{\circ }$$
To solve this equation sum of all the angles are equal to $${360}^{\circ }$$. On making an equation of sum of all angles.
$$\mathrm{\angle }AOB+\mathrm{\angle }BOC+\mathrm{\angle }COD+\mathrm{\angle }DOE+\mathrm{\angle }EOA={360}^{\circ }$$
On putting all the values from the given things.
$${47}^{\circ }+x^{\circ }+{83}^{\circ }+{92}^{\circ }+{75}^{\circ }={360}^{\circ }$$
On further adding all the angles.
$$x^{\circ }+{297}^{\circ }={360}^{\circ }$$
Taking $${297}^{\circ }$$ to the other side.
$$x^{\circ }={360}^{\circ }-{297}^{\circ }$$
On further solving
$$x^{\circ }={63}^{\circ }$$

Hence, the value of the unknown angle is $${63}^{\circ }$$.

Note:To solve this type of question you must know the angles made by a single line incomplete revolution and the angle between two string lines and two perpendicular lines. And if all angles are given in terms of a single variable then try to find the value of that single variable. and apply that to all the relations of the angles and find the values of all known angles.