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SVEN [57.7K]
3 years ago
12

3. B ge 18cm A 60° 20cm с Calculate the size of angle ABC.

Mathematics
1 answer:
uysha [10]3 years ago
8 0

Answer:

Step-by-step explanation:

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In the figure above, PQRS is a circle. If PQT and SRT<br>are straight lines, find the value of x.
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Given:

PQRS is a circle, PQT and SRT  are straight lines.

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Since PQRS is a circle, PQT and SRT  are straight lines, therefore, PQRS isa cyclic quadrilateral.

We know that, sum of opposite angles of a cyclic quadrilateral is 180 degrees.

m\angle SPQ+m\angle QRS=180^\circ

81^\circ+m\angle QRS=180^\circ

m\angle QRS=180^\circ-81^\circ

m\angle QRS=99^\circ

Now, SRT  is a straight line.

m\angle QRT+m\angle QRS=180^\circ             (Linear pair)

m\angle QRT+99^\circ=180^\circ

m\angle QRT=180^\circ-99^\circ

m\angle QRT=81^\circ               ...(i)

According to the Exterior angle theorem, in a triangle the measure of an exterior angle is equal the sum of the opposite interior angles.

Using exterior angle theorem in triangle QRT, we get

m\angle PQR=m\angle QRT+m\angle QTR

x=81^\circ+22^\circ

x=103^\circ

Therefore, the value of x is 103 degrees.

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