Advertisement Remove all ads

If Below Fig, ∠Aof and ∠Fog Form a Linear Pair.∠Eob = ∠Foc = 90° and ∠Doc = ∠Fog = ∠Aob = 30°(I) Find the Measures of ∠Foe, ∠Cob and ∠Doe.(Ii) Name All the Right Angles. - Mathematics

Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads

If below fig, ∠AOF and ∠FOG form a linear pair.


∠EOB = ∠FOC = 90° and ∠DOC = ∠FOG = ∠AOB = 30°
(i) Find the measures of ∠FOE, ∠COB and ∠DOE.
(ii) Name all the right angles.
(iii) Name three pairs of adjacent complementary angles.
(iv) Name three pairs of adjacent supplementary angles.
(v) Name three pairs of adjacent angles.

Advertisement Remove all ads

Solution

(i)  `∠`FOE = x, `∠`DOE = y and `∠`BOC = z sat

Since `∠`AOF , `∠`FOG is Linear pair

⇒`∠`AOF + 30° = 180°              [`∠`AOF + `∠`FOG = 180° and `∠`FOG = 30°]

⇒ `∠`AOF = 180° - 30°

⇒ `∠`AOF = 150°

⇒ `∠` AOB + `∠`BOC + `∠`COD + `∠`DOE + `∠`EOF = 150°

⇒ 30° + z + 30° + y + x = 150°

⇒ x + y + z = 150° - 30° - 30°

⇒ x + y + z = 90°                          .....(1)

Now `∠`FOC = 90°

⇒ `∠`FOE + `∠`EOD + `∠`DOC = 90°

⇒ x + y + 30° = 90°

⇒ x + y = 90° - 30°

⇒ x + y = 60°                              .....(2)

Substituting (2) in (1)

x + y + z = 90°

 60 + z = 90° Þ z = 90° - 60° = 30°

i.e., `∠`BOC = 30°

Given `∠`BOE = 90°

`∠`BOC + `∠`COD + `∠`DOE = 90°

⇒ 30° + 30° + `∠`DOE = 90°

⇒ `∠`DOE = 90° - 60° = 30°

∴ `∠`DOE = x = 30°

Now, also we have

x + y = 60°

⇒ y = 60° - x = 60° - 30° = 30°

`∠`FOE = 30

(ii) Right angles are

`∠`DOG, `∠`COF , `∠`BOF , `∠`AOD

(iii) Three pairs of adjacent complementary angles are

`∠`AOB, `∠`BOD;

`∠`AOC, `∠`COD;

`∠`BOC, `∠`COE

(iv) Three pairs of adjacent supplementary angles are

`∠`AOB, `∠`BOG;

`∠`AOC, `∠`COG;

`∠`AOD, `∠`DOG.

(v) Three pairs of adjacent angles

`∠`BOC, `∠`COD;

`∠`COD, `∠`DOE;

`∠`DOE, `∠`EOF ,

Concept: Pairs of Angles
  Is there an error in this question or solution?

APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 10 Lines and Angles
Exercise 10.2 | Q 18 | Page 16

Video TutorialsVIEW ALL [1]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×