Question

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Answer 1

Answer:

Hi,

1A: We need to take SRPQ as a trapezium to make it more clear... As you can see that it is a trapezium inside a circle, don't consider the circle as we have nothing to do with it...

PSQR - Trapezium,

The sum of total angles in the trapezium is 360 degrees,

So we only one angle in the trapezium ; RQP = 75 degrees,

So let's now consider the figure the whole figure except for the circle,

You can see a triangle,

The sum of the total angles in the traingle = 180 degrees,

So the angle: QPS = 180 - PQT + STR

= 180 - 75 + 30

= 75 degrees......

Now let's again go back to the trapezium.... Know we know the 2 angles in the trapezium & you should now that the next 2 angles should be of the same length.... 360 - 75 + 75 = 210/2 = 105 degrees...This is for the angles both PSR & QRS are opp. and equal...We have solved for the 3 questions..

PSR = QRS = 105 degrees,

QPS = 75 degrees,

4A; The Isoceles triangle theorem states that :

[In our triangle]

There should be 2 equal angles in the triangle....As we know from the starting that S = R .

Hence, proved that STR is an Isoceles traingle.

But if you carefully look, then you will see that the point S&R has two sides thst is covered up by the circle has two sides and we found only the angle that is facing the left side....either way S = R

SExpert Verififed Answer* by Venkatarajesh75