Question

Abcd is a rhombus if angle bca is 35 find angle adc

Answer 1

you can see the answer in this photo

Answer 2

In triangles abc and acd,
bc = ad [opposite sides of a rhombus]
ac is common to both
ab = dc [opposite sides of a rhombus]
therefore,
triangle abc is congruent to triangle acd
=> angle bca = angle acd
but angle bca = 35°
therefore, angle c = angle bca + angle acd
= 35° + 35° [angle bca = angle acd]
= 70°

now in rhombus abcd,
angle a = angle c [opposite angles of rhombus]
angle a = 70°

Also,
angle bac = angle dac
but angle bac + angle dac = angle a
=> angle bac + angle bac = angle a
[angle bac = angle dac]
=>2 × angle bac = angle a
=> angle bac = 70° / 2
=> angle bac = 35°

In triangle abc,
by angle sum property,
angle bac + angle bca + angle abc = 180°
=> 35° + 35° + angle abc = 180°
=> 70° + angle abc = 180°
=> angle abc = 180°-70°
=> angle abc = 110°
or angle b = 110°
therefore angle b = angle d = 110 °
[opposite angles of a rhombus]
therefore angle adc = 110°
[angle adc is same as angle d]