Advertisement Remove all ads

Prove that If the Two Arms of an Angle Are Perpendicular to the Two Arms of Another Angle, Then the Angles Are Either Equal Or Supplementary - Mathematics

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

Prove that if the two arms of an angle are perpendicular to the two arms of another angle, then the angles are either equal or supplementary

Advertisement Remove all ads

Solution

Consider be angles AOB and ACB

Given OA  ⊥ AC, OB ⊥ BC

To prove: `∠`AOB = `∠`ACB (or)

`∠`AOB + `∠`ACB = 180°

Proof:- In a quadrilateral                        [Sum of angles of quadrilateral]

⇒`∠`A + `∠`O + `∠`B + `∠`C = 360°

⇒ 180 + `∠`O + `∠`C = 360°

⇒ `∠`O + `∠`C = 360 -180 = 180°

Hence, `∠`AOB + `∠`ACB = 180°        ......(i )

Also,

`∠`B + `∠`ACB = 180°              ......(i )

Also,

`∠`B + `∠`ACB = 180°         ......(i )

Also,

`∠`B + `∠`ACB = 180°

⇒ `∠`ACB = 180° - 90°

⇒`∠`ACB = 90°        .....(ii)

From (i) and (ii)

∴`∠`ACB = `∠`AOB = 90°

Hence, the angles are equal as well as supplementary

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 10.4 | Q 23 | Page 49

Video TutorialsVIEW ALL [1]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×