![]() (2) The measure of angle S is 40 degrees -> consider two cases: S=R=40 and T=100 AND S=40 and R=T=70. (1) The measure of angle T is 100 degrees -> since no other angle can be equal to 100 degrees (because in this case the sum of the angles will be more than 180 degrees) then the other two angles, R and S, are equal: R=(180-100)/2=40. Triangle RST is isosceles means that two of its angles are equal. In isosceles triangle RST what is the measure of angle R? ![]() With (1) good and (2) no good, answer is (A). Since you have MULTIPLE possibilities with statement (2), then you do not have enough information to definitively say what the answer is. In other words, you'd have two possibilities: OR you can have another angle that is also 40 degrees and the third angle would add up to 180. Well, what possibilities are there? You could have one 40 degrees and then the other two angles are equivalent and all 3 add up to 180. Statement (2) is just telling us that one angle is 40 degrees. Mathematically, 180 - 100 = 80 and then divide that by 2 to get 40 degrees. In other words, the other 2 angles combined must equal the difference between 180 and 100. So the only choice that makes sense is to have the other two angles equal and everything adds to 180. ![]() Well, it's impossible for one of the other angles to also be 100 degrees, because that would exceed that total of 180 degrees possible in a triangle. So either one of the other angles also equals 100 degrees, or the other two angles not mentioned are equivalent. You already know an entire triangle = 180 degrees. With statement (1), you are told measure of angle T is 100 degrees. The keyword is "isosceles"-which means 2 sides are the same and also.2 angles are the same This is a fairly one simple one that you should spend no more than 30 seconds on. ![]()
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