Chapter 2: Q22. (page 71)

In the diagram, $\vec{O B}$ bisects $∠ A O C$ and $\overset{\leftrightarrow}{E C} ⊥ \overset{\leftrightarrow}{O D}$ .
Find the value of x.
$m ∠ 1 = 2 x$ , $m ∠ 2 = 6 x + 2$ .

Short Answer

Expert verified

The value of xis 11.

Step by step solution

Step 1. Observe the given diagram.

The given diagram is:

Step 2. Write the relation between the angles ∠1 and ∠2.

As, $\overset{\leftrightarrow}{E C} ⊥ \overset{\leftrightarrow}{O D}$ , therefore the lines EC and OD are perpendicular lines.

Therefore, by using the definition of perpendicular lines it can be said that the measures of the angle $∠ D O E$ is $90 °$ .

That implies, $m ∠ D O E = 90 °$ .

Now, by using the angle addition postulate it can be said that $m ∠ D O E = m ∠ 1 + m ∠ 2$ .

Therefore, the relation between the angles ∠1 and ∠2 is:

$m ∠ D O E = m ∠ 1 + m ∠ 2$

$90 = m ∠ 1 + m ∠ 2$

Step 3. Find the value of x.

As, $m ∠ 1 + m ∠ 2 = 90 °$ , $m ∠ 1 = 2 x$ and $m ∠ 2 = 6 x + 2$ .

Therefore, the value of x is given by:

role="math" localid="1646589364482" $m ∠ 1 + m ∠ 2 = 90 °$

$2 x + 6 x + 2 = 90 °$

$8 x + 2 = 90 °$

$8 x = 90 ° - 2$

$8 x = 88 °$

$x = \frac{88}{8}$

$x = 11$

Therefore, the value of x is 11.

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In the diagram, $\vec{O B}$ bisects $∠ A O C$ and $\overset{\leftrightarrow}{E C} ⊥ \overset{\leftrightarrow}{O D}$ .
Find the value of x.
$m ∠ 1 = 2 x$ , $m ∠ 2 = 6 x + 2$ .

Short Answer

Step by step solution

Step 1. Observe the given diagram.

Step 2. Write the relation between the angles ∠1 and ∠2.

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∠1=2x, m∠2=6x+2.

Short Answer

Step by step solution

Step 1. Observe the given diagram.

Step 2. Write the relation between the angles ∠1 and ∠2.

Step 3. Find the value of x.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Calculus

Discrete Mathematics

Geometry

Probability and Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In the diagram, $\vec{O B}$ bisects $∠ A O C$ and $\overset{\leftrightarrow}{E C} ⊥ \overset{\leftrightarrow}{O D}$ .
Find the value of x.
$m ∠ 1 = 2 x$ , $m ∠ 2 = 6 x + 2$ .