Question

In Fig Find Angle X, Y ,Z.

Answer 1

Given:

• Two lines are interesting each other.
• Measure of one of the angle is 50°.

To Find:

• The values of x , y and z .

Concept Used:

• We will make use if concept of Vertically opposite angles .
• We will make use of measure of angle of a straight line .

Answer:

Some points to be remembered here,

• Vertically opposite angles are equal.
• Measure of angle of a straight line is 180°.

(For figure refer to attachment)

Now , $\bf{\angle AOC }$ and $\bf{\angle BOD }$ are Vertically opposite angles ,

Hence $\bf{\angle AOC=\angle BOD = 55^{\circ} }$

So , $\bf{\angle BOD = x = 55^{\circ} }$

$\rule{200}4$

Now , $\sf{\angle AOC }$ and $\sf{\angle AOD }$ are angles of a straight line.

Hence , $\bf{\angle AOC +\angle AOD =180^{\circ} }$

$\sf{\implies 55^{\circ}+\angle AOD =180^{\circ}}$

$\sf{\implies +\angle AOD =180^{\circ}-55^{\circ}}$

$\bf{\leadsto \angle AOD = 125^{\circ}}$

$\rule{200}4$

Now , $\bf{\angle AOD }$ and $\bf{\angle BOC }$ are Vertically opposite angles ,

Hence $\bf{\angle AOD=\angle BOC = 125^{\circ} }$

So , $\bf{\angle AOD = y= z = 125^{\circ} }$

Hence measure of

• x is 55°.
• y is 125°.
• z is 125° .

Answer 2

Step-by-step explanation:

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