Question

In the given figure; AOC is a straight line. If angle AOB $={50}^{\circ }$, angle AOE $={90}^{\circ }$ and angle COD$={25}^{\circ }$; find the measure of:
(1) angle BOC
(2) angle EOD
(3) obtuse angle BOD
(4) reflex angle BOD

Answer 1

(1) Given
AOC is a straight line
$\angle AOB={50}^{\circ }\angle AOE={90}^{\circ }\angle COD={25}^{\circ }$
To find the measure of $\angle BOC$,
$\angle AOB+\angle BOC={180}^{\circ }$ (Linear pair of angle )
${50}^{\circ }+\angle BOC={180}^{\circ }$
Our further calculation, we get
$\angle BOC={180}^{\circ }-{50}^{\circ }$
$\angle BOC={130}^{\circ }$
(2)
$\text{To find the measure}\angle EOD\angle EOD+\angle COD={90}^{\circ }(Since\angle AOE={90}^{\circ })\angle EOD+{25}^{\circ }={90}^{\circ }\angle EOD={90}^{\circ }-{25}^{\circ }Weget,\angle EOD={65}^{\circ }$
(3)
To find the measure of obtuse angle BOD,
$\angle BOD=\angle BOC+\angle COD\text{Substituting the value of}\angle BOCand\angle COD,Weget,\angle BOD={130}^{\circ }+{25}^{\circ }Weget,\angle BOD={155}^{\circ }$
(4)
To find the measure of reflex angle BOD
reflex $\angle BOD={360}^{\circ }-\angle BOD={360}^{\circ }-{155}^{\circ }Weget,reflex\angle BOD={205}^{\circ }$