Chapter 6: Q8. (page 212)

For the following figure, find the measures of $∠ 1, ∠ 2, ∠ 3$ and $∠ 4$ .

Short Answer

Expert verified

The measures of the angles $∠ 1, ∠ 2, ∠ 3$ and $∠ 4$ are role="math" localid="1638195243372" $60 °, 75 °, 45 °$ and role="math" localid="1638195267206" $60 °$ .

Step by step solution

Step 1. Apply the concept of angles.

In a triangle sum of all the angles of the triangles is 180 degrees.

Alternate opposite angles of two lines are equal.

Step 2. Check the figure.

Consider the figure.

As alternate opposite angles of two lines are equal then the angles $∠ 1, ∠ 3$ as follows:

role="math" localid="1638194671820" $∠ 1 = 60 °$

$∠ 3 = 45 °$

Step 3. Find the angle.

Since the sum of all angles of the triangles is 180 degrees thus find the angle as follows:

$\begin{matrix} 60 ° + 45 ° + ∠ 2 = 180 ° \\ 105 ° + ∠ 2 = 180 ° \\ ∠ 2 = 180 ° - 105 ° \\ ∠ 2 = 75 ° \end{matrix}$

Step 4. Step description.

As the sum of all the angles on one side of the triangle is 180 degrees thus find the angles as follows:

$\begin{matrix} ∠ 2 + ∠ 3 + ∠ 4 = 180 ° \\ 75 ° + 45 ° + ∠ 4 = 180 ° \\ ∠ 4 = 180 ° - 120 ° \\ ∠ 4 = 60 ° \end{matrix}$

Hence, the measures of $∠ 1, ∠ 2, ∠ 3$ androle="math" localid="1638195217948" $60 °, 75 °, 45 °$ is and $60 °$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

For the following figure, find the measures of $∠ 1, ∠ 2, ∠ 3$ and $∠ 4$ .

Short Answer

Step by step solution

Step 1. Apply the concept of angles.

Step 2. Check the figure.

Step 3. Find the angle.

Step 4. Step description.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Theoretical and Mathematical Physics

Probability and Statistics

Applied Mathematics

Pure Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

For the following figure, find the measures of ∠1,∠2,∠3and ∠4.

Short Answer

Step by step solution

Step 1. Apply the concept of angles.

Step 2. Check the figure.

Step 3. Find the angle.

Step 4. Step description.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Theoretical and Mathematical Physics

Probability and Statistics

Applied Mathematics

Pure Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

For the following figure, find the measures of $∠ 1, ∠ 2, ∠ 3$ and $∠ 4$ .