Question -
Answer -
It is known that the sum of the opposite angles of a cyclic quadrilateral is 180o
Thus, we have
тИаC +тИаA = 180
4y + 20тИТ 4x = 180
тИТ 4x + 4y = 160
x тИТ y = тИТ 40 тАжтАжтАжтАжтАж(1)
And, тИаB + тИаD = 180
3y тИТ 5 тИТ 7x + 5 = 180
тИТ 7x + 3y = 180 тАжтАжтАж..(2)
Multiplying 3 to equation (1), we get
3x тИТ 3y = тИТ 120 тАжтАжтАж(3)
Adding equation (2) to equation (3), we get
тИТ 7x + 3x = 180 тАУ 120
тИТ 4x = 60
x = тИТ15
Substituting this value in equation (i), we get
x тИТ y = тИТ 40
-yтИТ15 = тИТ 40
y = 40-15
= 25
тИаA = 4y + 20 = 20+4(25) = 120┬░
тИаB = 3y тИТ 5 = тИТ 5+3(25) = 70┬░
тИаC = тИТ 4x = тИТ 4(тИТ 15) = 60┬░
тИаD = 5-7x
тИаD= 5тИТ 7(тИТ15) = 110┬░
Hence, all the angles are measured.