Chapter 2: Q23. (page 71)

In the diagram, $\vec{OB}$ bisects $∠ AOC$ and $\overset{\leftrightarrow}{EC} ⊥ \overset{\leftrightarrow}{OD}$ .
Find the value of x.
m∠2 = 6x + 9, m∠5 = 2x + 49

Short Answer

Expert verified

The value of x is 10.

Step by step solution

Step 1. Observe the given diagram.

The given diagram is :

Step 2. Write the relation between the angles ∠2 and ∠5.

From the given diagram it can be noticed that the angles∠2and∠5are the vertical angles.

Therefore, by using the theorem for vertical angles it can be said that the angles∠2and∠5have the same measure.

That implies, $m ∠ 2 = m ∠ 5$ .

Therefore, the relation between the angles ∠2 and ∠5 is $m ∠ 2 = m ∠ 5$ .

Step 3. Find the value of x.

As, m∠2 =m∠5, m∠2 =6x + 9 andm∠5 = 2x + 49.

Therefore, the value of x is given by :

$m ∠ 2 = m ∠ 5$

$6 x + 9 = 2 x + 49$

$6 x - 2 x = 49 - 9$

$4 x = 40$

$x = \frac{40}{4}$

$x = 10$

Therefore, the value of x is 10.

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In the diagram, $\vec{OB}$ bisects $∠ AOC$ and $\overset{\leftrightarrow}{EC} ⊥ \overset{\leftrightarrow}{OD}$ .
Find the value of x.
m∠2 = 6x + 9, m∠5 = 2x + 49

Short Answer

Step by step solution

Step 1. Observe the given diagram.

Step 2. Write the relation between the angles ∠2 and ∠5.

Step 3. Find the value of x.

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In the diagram, OB→bisects ∠AOCand EC↔⊥OD↔.Find the value of x.m∠2 = 6x + 9, m∠5 = 2x + 49

Short Answer

Step by step solution

Step 1. Observe the given diagram.

Step 2. Write the relation between the angles ∠2 and ∠5.

Step 3. Find the value of x.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Calculus

Statistics

Discrete Mathematics

Theoretical and Mathematical Physics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

In the diagram, $\vec{OB}$ bisects $∠ AOC$ and $\overset{\leftrightarrow}{EC} ⊥ \overset{\leftrightarrow}{OD}$ .
Find the value of x.
m∠2 = 6x + 9, m∠5 = 2x + 49