Question

in figure ABCD is a parallelogram in which <ADC = 60° and <ACB =70° . find the measure of <DCB, <CAB and <DAC​

Answer 1

Answer:

ABCD is a parallelogram.

Hence , AD || BC , AC is the transversal

→ <DAC = <ACB [ Alternate angles ]

→ <DAC = 70⁰

In triangle ADC ,

<DAC + <ADC + <ACD = 180⁰

→ 70 + 60 + <ACD = 180

→ 130 + <ACD = 180

→ <ACD = 180 - 130

→ <ACD = 50⁰

Now, <DCB = <ACD + <ACB

= 50 + 70

→ <DCB = 120⁰

AB || DC , AC is the transversal

→ <ACD = <CAB [ Alternate angles ]

→ <CAB = 50⁰

Therefore, <DCB = 120⁰ , <CAB = 50⁰ and <DAC = 70⁰