Question

if ABCD is a rhombus, find the measure of angle ADC, given that angle BAC is 55

Answer 1

As we know that the diagonal are the angel bisector of rhombus.
So, diagonal AC bisects ∠BAD

∴∠BAD = 2∠BAC = 2×55° = 110°

Now, ∠BAD + ∠ADC = 180° ( parallel line property)
⇒∠ADC = 180°- 110° = 70°

Answer 2

Answer:

Step-by-step explanation:

Given :-

BAC = 55°

To Find :-

∠ ADC

Formula to be used :-

Angle sum property and Opposite angle of a rhombus are equal.

Solution :-

In rhombus ABCD

AB = AC

⇒ ∠BAC = ∠BCA = 55°

In ∆ ABC, we have

⇒ BAC + BCA + ABC = 180° [∠ sum property]

⇒ 55° + 55° + ABC = 180°

⇒ 110° + ABC = 180°

⇒ ABC = 70°

As we know that opposite angle of a rhombus are equal.

⇒ ABC = ADC = 70°

Hence, measure of ADC is 70°.