Hot Lava Mama Posted March 24, 2014 Share Posted March 24, 2014 Can someone help us figure out how to get to the answer? Here's the best I can do for a picture: B D A C Imagine there are lines as follows: AB to BC to AC to make a triangle. Then, AD to DC to AC to make a smaller triangle within the bigger one sharing the same bottom line of AC. Given: line AB congruent to line BC, angle DAC congruent to angle BCD, measure of angle B is 50. Find measure of angle ADC. Here is what we figured out: since AB = BC, the triangle is an isosceles, so angles BAC = BCA. Therefore, angle BAD also = to DCA. But we can't go any further. The answer is 115, but we can't figure out how they got there. Anyone a geometry wizard? :) Hot Lava Mama Quote Link to comment Share on other sites More sharing options...
MicheleinMN Posted March 25, 2014 Share Posted March 25, 2014 Because AB = BC the corner angles for each line to are equal. Angle CAB = ACB with angle B= 50 (given) means that each angle is 65 (180 - 50=130 and that divided by 2 equals 65). We also know that the corner angles are bisected by AD and CD meaning they are 1/2 of the original angles, so they equal 32.5 each or 65 total. 180 - 65 = 115. Does that help? Quote Link to comment Share on other sites More sharing options...
EKS Posted March 25, 2014 Share Posted March 25, 2014 You could also do it this way: You know that angle BAC and angle BCA are each 65 degrees. Say that angle DAC (and angle BCD)=x. That means that angle DCA=65-x. Therefore angle ADC=180-(x+65-x) which is 115. Quote Link to comment Share on other sites More sharing options...
Hot Lava Mama Posted March 25, 2014 Author Share Posted March 25, 2014 Thanks! That's it! :) Quote Link to comment Share on other sites More sharing options...
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