Chapter 3: Q12 (page 80)

If $m ∠ 4 = 2 m ∠ 3$ find $m ∠ 6$

Short Answer

Expert verified

Measurement of $∠ 6$ is 60

Step by step solution

Step 1. Observations from figure

Arrowheads are shown on lines $I$ and $P$ , so these lines are parallel
Line $t$ is transversal to the parallel lines $I$ and $P$

Step 2. Find m angle 3

$∠ 3$ and $∠ 4$ forms linear pair, so sum of these angles is 180

$\begin{matrix} m ∠ 3 + m ∠ 4 = 180 \\ m ∠ 3 + 2 m ∠ 3 = 180 \end{matrix}$

$\begin{matrix} 3 m ∠ 3 = 180 \end{matrix}$

$m ∠ 3 = \frac{180}{3}$

$m ∠ 3 = 60$

- Find m angle 6

$∠ 3$ and data-custom-editor="chemistry" $∠ 6$ forms a pair of alternate interior angles, so measurement of these angles are equal. $m ∠ 3 = m ∠ 6$

Thus, $m ∠ 6 = 60$

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Statement	Reason
1. $k ∥ l$	Given
2. $∠ 3 ≅ ∠ 2$	If two parallel lines are cut by transversal then alt. int. $∠ s$ are $≅$
3. $∠ 1 ≅ ∠ 3$	Vert. $∠ s$ are $≅$
4. $∠ 1 ≅ ∠ 2$	Transitive Property

If $m ∠ 4 = 2 m ∠ 3$ find $m ∠ 6$

Short Answer

Step by step solution

Step 1. Observations from figure

Step 2. Find m angle 3

- Find m angle 6

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If m∠4=2m∠3find m∠6

Short Answer

Step by step solution

Step 1. Observations from figure

Step 2. Find m angle 3

- Find m angle 6

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Mechanics Maths

Geometry

Theoretical and Mathematical Physics

Applied Mathematics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

If $m ∠ 4 = 2 m ∠ 3$ find $m ∠ 6$