Chapter 6: Q20. (page 205)

Complete the proof $m ∠ 2 > m ∠ 4$ if $m ∠ 2 > m ∠ 1$ is 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. $∠ 3 ≅ ∠ 4$ , or $m ∠ 3 = m ∠ 4$	Vertically opposite angles
e. $m ∠ 2 > m ∠ 4$	From c.

Step by step solution

Step 1. Point the lines in the given figure

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.

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

Short Answer

Step by step solution

Step 1. Point the lines in the given figure

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

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

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

Short Answer

Step by step solution

Step 1. Point the lines in the given figure

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

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Decision Maths

Probability and Statistics

Statistics

Applied Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

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