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Chapter 6: Q20. (page 205)

Complete the proof m∠2>m∠4if m∠2>m∠1is given.

Short Answer

Expert verified

Statement

Reason

a.m∠2>m∠1

Given

b.m∠1>m∠3

Exterior angle is greater than any interior angle of the triangle

c.m∠2>m∠3

From a.

d.∠3≅∠4, orm∠3=m∠4

Vertically opposite angles

e.m∠2>m∠4

From c.

Step by step solution

01

Step 1. Point the lines in the given figure

02

Step 2. Define vertically opposite angles and interior, exterior angles

Pair of opposite angles formed by intersecting lines.

Therefore, angles 3 and 4 are vertically opposite angles. Angle 1 and 4 are exterior angles of the triangle APQ and 3 is an interior angle.

03

Step 3. Prove that angle 2 is greater than angle 4

Proof:

m∠2>m∠1 …… (1) (Given)

m∠1>m∠3 (Exterior angle is greater than any interior angle of the triangle)

m∠2>m∠3 …… (2) (From equation (1))

m∠4=m∠3 (Vertically opposite angles)

m∠2>m∠4 (From equation (2))

Hence proved m∠2>m∠4.

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