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Question
Calculate the angles D and B of the quadrilateral shown in the figure.
Calculate the angles D and B of the quadrilateral shown in the figure.
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Solution
In triangle ADC,
Let ∠ODC = x
∠DAC + ∠ADC + ∠DCA = 180°
65 + 40 + x + 30 = 180
x = 45
∠ADC = x + 40 = 95°
As quadrilateral ABCD is cyclic then the summation of measure of opposite angles should be 180°.
Thus here
∠ADC + ∠ABC = 180°
95 + ∠ABC = 180
∠ABC = 85°
Let ∠ODC = x
∠DAC + ∠ADC + ∠DCA = 180°
65 + 40 + x + 30 = 180
x = 45
∠ADC = x + 40 = 95°
As quadrilateral ABCD is cyclic then the summation of measure of opposite angles should be 180°.
Thus here
∠ADC + ∠ABC = 180°
95 + ∠ABC = 180
∠ABC = 85°
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