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Question

post-18057

Please help me with this question. Thank you in advance.

Answer

angle RBC = angle BCD = angle CDE(alt angles)
8x – 24 = 64
x = 11

angle BCR = angle BCD (BC is the angle bisector of angle RCD)
3y + 10 = 8(11) – 24
y = (54 – 10)/3 = 18

angle BCR = angle DEC (corresponding angles)
angle DEC = 3(18) x 10 = 64
angle DEC + angle DES = 180 degrees (sum of angles on a str line)
64 + 5z – 19 = 180
z = (180 – 45)/5 = 27
or
angle BCR + angle BCD + angle DCS (sum of angles on a str line)
3(18) + 10 + 8(11) – 24 + angle DCS = 180
angle DCS = 52 degrees
angle DES = angle DCS + angle CDE (ext angle equals to 2 int angles)
5x – 19 = 52 + 64 = 116
z = (116 + 19)/5 = 27

Ans : x = 11, y = 18 and z = 27.

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