Question

Q53. In the following figure find x*
90
60
D
90
B40
O (a) 40 degrees
O (b) 140 degrees
O (c) 100 degrees
O
(d) 80 degrees​

Answer 1

ANSWER

Let the given triangle be ABC such that ∠ABC=36. A line through C meets AB at D.

Now, In △DBC,

DB=DC (Given)

hence, ∠DBC=∠DCB=36

∘

(Isosceles triangle property)

Sum of angles of triangle = 180

∠DBC+∠DCB+∠CDB=180

36+36+∠CDB=180

∠CDB=108

Now, ∠ADC=180−∠ADB

∠ADC=180−108

∠ADC=72

∘

in △ADC,

∠ADC=∠DAC=72

∘

(Isosceles triangle property, AC= CD is given)

Sum of angles = 180

∠ADC+∠CAD+∠ACD=180

72+72+x=180

x=180−144

x=36

∘