Question

In the figure shown below, if AC=BD, AD=CD and ∠ACD=40°, then what could be the measure of ∠BAC?

Answer 1

Answer:

Given:AC=BD, AD=CD and ACD=40°

To Prove: BAC

Proof: AC=BD(Given)

AD=CD(Given)

ACD+BAC=180°

40°+BAC=180°

BAC=180°-40°

BAC=140°

Answer 2

Answer:10

Step-by-step explanation:

>If AD = DC, then Angle ACD = Angle DAC. (Rule: Equal sides are opposite equal angles.)

> We know that Angle ACD = 40. That means that angle DAC is also 40.

> Because a line is made up of 180 degrees, Angle ACB must be 140.

> The question tells us that AC = BD. This means that BC < AC. If that's the case, the angle opposite AC (ABC) must be greater than the angle opposite BC (BAC).

>The answer can't be 20, because then the two remaining angles would BOTH be 20. It can't be 30, because then BAC would be bigger than ABC. The answer must be 10 degrees.