Question

In the adjoining figure, AC = CD = BD and ∠CBD = 40°. Find ∠ACD.

Answer 1

Given: AC = CD = BD and ∠CBD = 40°.

Step-wise calculation:

1. In triangle BCD,

BD = CD

So, base angles are equal: 

∠CBD

= ∠BCD

= 40°

2. Hence, ∠BDC

= 180° – 40° – 40° 

= 100°

3. From the figure,

D lies on line AB. 

So, ∠ADC and ∠BDC are supplementary. 

Therefore, ∠ADC

= 180° – 100° 

= 80°

4. In triangle ACD,

AC = CD

So, ∠CAD

= ∠ADC

= 80°

5. Thus, ∠ACD

= 180° – 80° – 80° 

= 20°