Finding Missing Angle Using the Concept of Transversal :
Here we are going to see some example problems of finding missing angles using the concept of transversal.
Question 1 :
In the figure, AB is parallel to CD, find x
Let us draw a line passing through T and parallel to AB and CD.
The lines AB and TS are parallel and TA is a transversal.
<ATS + <TAB = 180
<ATS + 140 = 180
<ATS = 180 - 140 = 40 --(1)
In a same way
<TCD + <CTS = 180
150 + <CTS = 180
<CTS = 180 - 150 = 30 ---(2)
(1) + (2) ==> 40 + 30 = 70
Hence the value of x is 70.
Now we have drawn a line passing through x and it is parallel to AB and CD.
<PRB + <ABR = 180
<PRB + 48 = 180
<PRB = 180 - 48
<PRB = 132 ----(2)
In the same way,
<PRD + <CDR = 180
<PRD + 24 = 180
<PRD = 180 - 24 = 156 ---(1)
(1) + (2) ==> 132 + 156 = 288
Hence the required angle is 288.
<BAD = <ADC (Alternative angles)
<ADC = 53
In triangle ECD,
<ECD + <CDE + <DEC = 180
38 + 53 + <DEC = 180
<DEC = 180 - 91
<DEC = 89
Hence the value of x is 89.
Question 2 :
The angles of a triangle are in the ratio 1 : 2 : 3, find the measure of each angle of the triangle.
The angles of triangle are x, 2x and 3x.
Sum of the interior angles of triangle = 180
x + 2x + 3x = 180
6x = 180
x = 180/6
x = 30
Hence the required angles are 30, 60 and 90.
After having gone through the stuff given above, we hope that the students would have understood, "Finding Missing Angle Using the Concept of Transversal"
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