Math, asked by aditi11choudhary22, 8 months ago

In the adjacent figure, DO and CO are the bisectors of angle D and angle C, respectively. Find angle DOC and angle A​

Attachments:

Answers

Answered by Anonymous
24

\blue\bigstarAnswer:

\angleDOC = 135° and \angleA = 150°

\blue\bigstar Given:

  • DO is the bisector of \angleD
  • CO is the bisector of \angleC
  • \angleADO = 20°
  • \angleDCO = 25°
  • \angleABC = 120°

\blue\bigstarTo find:

  • \angleDOC
  • \angleA

\blue\bigstar Solution:

\because DO is the bisector of \angleADC,

\therefore\boxed{\angle ADO \:=  \:\angle ODC \: = 20°\:}

In \triangleODC,

\because\angleODC + \angleDCO + \angleDOC = 180°

(Angle Sum Property Of A Triangle)

\implies 20° + 25° + \angleDOC = 180°

(By substituting their values)

\implies 45° + \angleDOC = 180°

\implies \angleDOC = 180° - 45°

\implies \boxed{\angle DOC\: = \:135°\:}

\therefore \angleDOC = 135°

So, \angleD = \angleADO + \angleODC

\implies \angleD = 20° + 20°

( \because \angleD is bisected, therefore the bisected angles are equal)

\implies \boxed{\angle D\: = 40°\:}

\therefore \angleD = 40°

\angleC = \angle OCD + \angle OCB

\impliesC = 25° + 25°

( \because \angleC is bisected, therefore the bisected angles are equal)

\implies \boxed{\angle C \:= 50°\:}

\therefore \angleC = 50°

Now in Quadrilateral ABCD,

\because \angle A + \angle B + \angleC + \angleD = 360°

( Angle Sum Property Of A Quadrilateral)

\implies \angleA + 120° + 50° + 40° = 360°

\implies \angleA + 210° = 360°

\implies \angleA = 360° - 210°

\implies \boxed{\angle A\:= \:150°\:}

\therefore \angleDOC = 135° and \angleA = 150°

\pink\bigstar Concepts Used:

  • Angle Sum Property Of A Triangle
  • Angle Sum Property Of A Quadrilateral
  • When an angle is bisected, then both the angles will be equal.
Answered by ramprit51
5

Step-by-step explanation:

hope it will help you

And please follow me and make me brainly

Attachments:
Similar questions