Question

From the figure given below write the measures of the following angles:



(1) m∠AOC = ________
(2) m∠AOD = ________
(3) m∠BOC = ________

Answer 1

(1) A pair of non-adjacent angles formed by the intersection of two straight lines is known as a pair of vertically opposite angles.
So, $\angle AOC$ and $\angle DOB$ are vertically opposite angles.
Because vertically opposite angles are of the same measure, m$\angle AOC$ = m$\angle DOB$ = 60°.


(2) A pair of adjacent angles whose outer arms are opposite rays is called a linear pair of angles.
Here, $\angle AOD$ and $\angle DOB$ form a linear pair.
Also, the sum of the measures of such angles is 180°.
∴ $\angle AOD$ + $\angle DOB$ = 180°
= $\angle AOD$ + 60° = 180°
= $\angle AOD$ = 180° – 60°
= $\angle AOD$ = 120°

(3) A pair of adjacent angles whose outer arms are opposite rays is called a linear pair of angles.
Here, $\angle BOC$ and $\angle DOB$ form a linear pair.
Also, the sum of the measures of such angles is 180°.
∴ $\angle BOC$+ $\angle DOB$ = 180°
= $\angle BOC$ + 60° = 180°
= $\angle BOC$ = 180° – 60°
= $\angle BOC$ = 120°