Chapter 9: Q15. (page 342)

a. Given: $\bar{W Z}$ is a diameter of $⊙ O;$
Prove: $m ∠ Z = n .$

Short Answer

Expert verified

The final answer is $m ∠ Z = n.$

Step by step solution

Step 1. Given information:

$\bar{W Z}$ is a diameter of circle and $m (W X) = m (X Y) = n$

Step 2. Concept used:

We use basic geometric and angle concept

Step 3. Applying the concept:

First let us draw $\bar{O Y}$ in the given figure.

Then $\bar{O Y}$ and $\bar{O Z}$ becomes radii of the circles $\Rightarrow \bar{O Y} = \bar{O Z}$

Since $m (X Y) = m ∠ X O Y = n$

Since $\bar{O X} | | \bar{Z Y}$ and $\bar{O Y}$ transverse line

$\Rightarrow m ∠ X O Y = m ∠ O Y Z = n$

and also $Δ O Z Y$ is isosceles triangles as $\bar{O Y} = \bar{O Z}$ then $m ∠ O Y Z = m ∠ O Z Y = n$

Hence, $m ∠ Z = n$

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a. Given: $\bar{W Z}$ is a diameter of $⊙ O;$
Prove: $m ∠ Z = n .$

Short Answer

Step by step solution

Step 1. Given information:

Step 2. Concept used:

Step 3. Applying the concept:

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a. Given:WZ¯is a diameter of ⊙O;Prove: m∠Z=n.

Short Answer

Step by step solution

Step 1. Given information:

Step 2. Concept used:

Step 3. Applying the concept:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Study anywhere. Anytime. Across all devices.

a. Given: $\bar{W Z}$ is a diameter of $⊙ O;$
Prove: $m ∠ Z = n .$