Question

answer the questions

Answer 1

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Answer:

Here we have to use ,

Angle sum property in triangle SOT and quadrilateral TOSR.

In trangle SOT,

a + b + 140 = 180

a + b = 40 ____________(1)

And,

Total angle at O = 360 ,

so, SOT+140 = 360

Hence , angle SOT of quadrilteral TOSR = 220 _____(2)

Step-by-step explanation:

Now applying it to the quadrilateral TOSR,

=> a + b + x + SOT = 360

=> 40 + x + 220 = 360                 [from equation 1&2 (a+b=40 & SOT=220)]

=> x = 100

Hence , angle x measures 100 degree.

Therefore answer is option [4] 100 .

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Answer 2

In triangle RST and triangle OST
angle RSO= angle OST=a
angle RST = angle RSO + angle OST
angle RTS1/2 = angle OST

angle RTO= angle OTS=b
angle RTS= angle RTO + angle OTS
angle RTS1/2= angle OTS

In triangle OST
Angle sum property
angle SOT + angle OST + angle OTS = 180°
140° + 1/2angle RST + 1/2angle RTS= 180°
1/2( angle RST + angle RTS ) = 40°
angle RST + angle RTS = 80°

In triangle RST
Angle sum property
angle SRT + angle RST + angle RTS = 180°
x + (angle RST + angle RTS) = 180
x + 80° = 180°
x= 100°

The answer is 4. 100°


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