Question

In figure, D is the mid-point of side BC of a ΔABC and ∠ABD = 50°. If AD = BD = CD, then find the measure of ∠ACD.
(a) 30° (b) 70° ( c) 80° (d) 40°

Answer 1

Step-by-step explanation:

one of the properties of isosceles Triangle the angles opposite to the same side are also same

Answer is 40°

I hope it helps

Answer 2

Given : D is the mid-point of side BC of a ΔABC and ∠ABD = 50°.

To Find :   AD = BD = CD, then find the measure of ∠ACD.

(a) 30° (b) 70° ( c) 80° (d) 40°

Solution:

AD = BD

=> ∠BAD = ∠ABD = 50°  ( in a triangle angles opposite to equal sides are equal )

∠BAD + ∠ABD + ∠ADB = 180°   using triangle angle sum

=> 50°  + 50°  + ∠ADB = 180°

=>  ∠ADB =  80°

∠ADB  = ∠ACD + ∠CAD   using Exterior angle theorem

=> 80° =  ∠ACD + ∠CAD

∠ACD =  ∠CAD  ∵   AD = CD

=> 80° =  ∠ACD + ∠ACD

=> 80° = 2 ∠ACD

=> 40° =  ∠ACD

the measure of ∠ACD  40°

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