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Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset Vaia Explanations$ Math

Student Edition · 227 pages

ISBN: 9780395977279

Chapter 3: Q11 (page 96)

Find the value of x.

Short Answer

Expert verified

The value of x is 75.

Step by step solution

01

Step 1. Label the given diagram.

The labelled diagram is:

02

Step 2. Description of step.

From the diagram it can be noticed that the angles $∠ A B E$ and $∠ A B C$ forms the linear pair.

Therefore, the sum of the angles $∠ A B E$ and $∠ A B C$ is $180 °$ .

Therefore, it can be obtained that:

$∠ A B E + ∠ A B C = 180 ° 140 ° + ∠ A B C = 180 ° ∠ A B C = 180 ° - 140 ° ∠ A B C = 40 °$

Therefore, the measure of the angle $∠ A B C$ is $40 °$ .

03

Step 3. Find the value of x.

Now, by using the exterior angle theorem it can be noticed that:

$∠ A B C + ∠ B A C = ∠ A C D$

Therefore, the value of x can be obtained as:

$∠ A B C + ∠ B A C = ∠ A C D 40 ° + 35 ° = x ° 75 ° = x ° \Rightarrow 75 = x$

Therefore, the value of x is 75.

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