Question

in figure 4 ABCD is a parallelogram in which angle ADC=60°and angle ACB=70°. Find the measures of angle DCB, angle CAB and angle DAC.

Answer 1

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In triangle CAD
AngleC+AngleA+AngleD=180°--------(1)[sum of the property of three sides of a triangle

In which angleCAD=70°[opp. angle of ACB,opp. Angles are equal]

Now substituting the values in eq(1)

AngleDCA+70°+60°=180°
AngleDCA+130°=180°
AngleDCA=180-130
AngleDCA=50°

Required angles are:
DCB=DCA+ACB==>50+70==>120°
CAB=50°[opp. angle of DCA]
DAC=70°

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