Chapter 5: Q24 (page 201)

In the diagram, $m ∠ VOZ = 90$ .
$\bar{OW}$ is an altitude of $△ VOZ$ .
$\bar{OX}$ bisects $∠ VOZ$ .
$\bar{OY}$ is a median of $△ VOZ$ .
Find the measures of the four numbered angles
$m ∠ Z = 30$

Short Answer

Expert verified

The measures of the four numbered angles $∠ 1, ∠ 2, ∠ 3$ and $∠ 4$ are $30 °, 15 °, 15 °$ and $30 °$ respectively.

Step by step solution

Step 1. Observe the given diagram.

The given diagram is:

Step 2. Description of step.

It is being given that $m ∠ V O Z = 90$ .

Therefore it can be obtained that:

$∠ 1 + ∠ 2 + ∠ 3 + ∠ 4 = 90 °$ .

As, $\bar{O X}$ bisects $∠ V O Z$ .

Therefore, $∠ V O Z = 2 ∠ V O X$ .

Therefore it can be obtained that:

$\begin{matrix} ∠ V O Z = 2 ∠ V O X \\ 90 ° = 2 ∠ V O X \\ \frac{90 °}{2} = ∠ V O X \\ 45 ° = ∠ V O X \end{matrix}$

Therefore, the measure of the angle $∠ V O X$ is .

As, bisects .

Therefore,

As, , therefore it can be obtained that:

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In the diagram, $m ∠ VOZ = 90$ .
$\bar{OW}$ is an altitude of $△ VOZ$ .
$\bar{OX}$ bisects $∠ VOZ$ .
$\bar{OY}$ is a median of $△ VOZ$ .
Find the measures of the four numbered angles
$m ∠ Z = 30$

Short Answer

Step by step solution

Step 1. Observe the given diagram.

Step 2. Description of step.

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In the diagram, m∠VOZ=90.OW¯ is an altitude of △VOZ.OX¯bisects ∠VOZ.OY¯is a median of △VOZ.Find the measures of the four numbered anglesm∠Z=30

Short Answer

Step by step solution

Step 1. Observe the given diagram.

Step 2. Description of step.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Theoretical and Mathematical Physics

Probability and Statistics

Decision Maths

Pure Maths

Statistics

Study anywhere. Anytime. Across all devices.

In the diagram, $m ∠ VOZ = 90$ .
$\bar{OW}$ is an altitude of $△ VOZ$ .
$\bar{OX}$ bisects $∠ VOZ$ .
$\bar{OY}$ is a median of $△ VOZ$ .
Find the measures of the four numbered angles
$m ∠ Z = 30$