Two right triangles are touching at the tips. The left triangle has the 90 degree angle to the bottom left, and 33 degrees on the bottom right. Based on this info, the other angle is 57 degrees. The right triangle has the right angle given, but it is on the top right, and the other two angles aren't given.
However, <A is formed when the right side of the right triangle is extended. The 33 degree angle's vertex is shared by the right triangle's, and an angle of 110 degrees is formed from the extended sides of the hypotenuse of the left triangle and a leg of the right triangle. The question, is, though, is to find the measure of <A.
My first answer was that m<A is 123 degeres, but it was marked wrong. I got that answer because one of the right triangle's angles was 33 degrees, by the Vertical Angles Theorem, and that was the angle with the shared vertex. With that said, I was thinking that the two triangles are congruent, since the angles are all equal. What exactly am I doing wrong?
(It'd be a lot easier if I could just have the figure there instead of describing it...I hope that's specific enough). Thanks much!
Based on the description you provided, I understand that you have two right triangles touching at the tips. One triangle has a 90 degree angle on the bottom left and a 33 degree angle on the bottom right. The other triangle has a right angle on the top right, but the other two angles are not given.
To find the measure of angle A, you need to use the information given about the extended sides and the angles formed. Let's break it down step by step:
1. In the left triangle, you have a 90 degree angle on the bottom left and a 33 degree angle on the bottom right. Therefore, the remaining angle can be found by subtracting the sum of the other two angles from 180 degrees:
Angle A = 180 - 90 - 33 = 57 degrees
2. Now, focus on the right triangle where the right angle is on the top right. You mentioned that when you extend the right side of the right triangle, it forms an angle A. We can work with that.
3. You stated that the shared vertex between the two triangles forms an angle of 33 degrees. Since angles opposite to each other are equal (vertical angles theorem), angle A in the right triangle is also 33 degrees.
4. The last piece of information is that an angle of 110 degrees is formed from the extended sides of the hypotenuse of the left triangle and a leg of the right triangle.
Now, here's where you made a slight mistake:
5. The two triangles are not congruent just because their angles are equal. To prove congruence, we need to have equal angles and equal sides. Since the sides are not given in this case, we cannot assume that the triangles are congruent.
6. However, we know that the angle opposite to angle A in the right triangle is 33 degrees, which we found in step 3. Therefore, angle A is indeed 33 degrees.
To summarize, the measure of angle A in the right triangle is 33 degrees, not 123 degrees as you initially thought.