Answer:
Since the fact that there will only be same degrees in angles in a shape with a side that equals another side, and there is two angles who's measures are equivalent, we know that the triangle must be isosceles
Step-by-step explanation:
First off, You must remember that in a triangle, the inside angles have a total of 180 degrees.
ADB equals also 72 degrees, and as the triangle is isosceles and since isosceles triangles have at least 2 equal angles, and AB = AD which makes ABD a isosceles triangle, ADB also equals 72 degrees as the line AD is equal to AB so ABD must equal to ADB. 72+72 = 144. 180 - 144 = 36. Basically, BAD = 36 degrees.
Also, since the two triangles form a bigger triangle, we know that BAD + ABC + BCD equals 180. 36 + 72 = 108. 180 - 108 = 72. So DBC + BCD must equal to 72. Also, there is a weak point. ADC is a straight angle, meaning it equals 180 degrees. The reason why ADC is a straight angle is because of the fact that a triangle has three sides and the sides must be a straight line except facing different directions and ADC is a side of the triangle ABC. since ADC equals 180, and we know that ADB equals 72, and 72+108 = 180, we know that BDC must equal to 108. Using what we know about the fact that the total of the a triangle's inner angles must equal to 180 and the fact that CDB equals 108, we know that BCD + DBC = 72. Since it said to show why BCD is isosceles, we know that BCD is isosceles(this is the few times when the question is actually the hint), we know that two of the angles are the same. 72/2 = 36, and 36+36+72+36 = 180, we know that BCD and DBC equals 36.
