Question
prove the following theorem : If two parallel lines are intersected by a transversal, the interior angles on either side of the transversal are supplementary.

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The following data gives the demand estimates of the Government of India, Department of Electronics for the personnel in the Computer sector during the Eighth Plan period (1990–95):
Qualifications
MCA (Masters in Computer Applications)
DCA (Diploma in Computer Applications
DCE (Diploma in Computer Engineering)
CL (Certificate Level Course)
ST (Short Term Course)
Personnel required
40600
181600
18600
670600
1802900
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A chord of length $30\ cm$ is drawn at a distance of $8\ cm$ from the centre of a circle.
Find out the radius of the circle.
In $\triangle\text{ABC},$ if $3\angle\text{A}=4\angle\text{B}=6\angle\text{C},$ calculate $\angle\text{A},\angle\text{B}$ and $\angle\text{C}.$
In a $\triangle\text{ABC},$ P and Q are respectively the mid points of AB and BC and R is the midpoint of AP. Prove that:
  1. $\text{ar}(\triangle\text{PBQ})=\text{ar}(\triangle\text{ARC}).$
  2. $\text{ar}(\triangle\text{PRQ})=\frac{1}{2}\text{ar}(\triangle\text{ARC}).$
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Image

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In the given figure, $AB\ ||\ CD$ and $EF\ ||\ GH$. Find the value of $x, y, z$ and $t$.