An isosceles, obtuse triangle has one angle with a degree measure that is 50% larger than the measure of a right angle. What is the measure, in degrees, of one of the two smallest angles in the triangle? Express your answer as a decimal to the nearest tenth.
50% larger than a right angle would be (90+45)° or 135°
That leaves 45° for the two equal angles, making each one 22.5°
An angle with measure $50\%$ larger than the measure of a right angle has measure $\frac{3}{2}\cdot 90^{\circ}=135^{\circ}$.
Thus the other two angles have a combined measure of $45^{\circ}$ Each one has a measure of
$$\frac{45^{\circ}}{2}=\boxed{22.5^{\circ}}$$
It is not cheat, it is not aops problem
Well, well, well, we have ourselves a mathematical conundrum. Let's see if we can put a funny spin on it, shall we?
So we have an isosceles, obtuse triangle. That means it's like one of those triangles that most people can't pronounce correctly. Isosceles, isosceles, how do you say it? No one knows!
Now, we know that one angle in this triangle is 50% larger than a right angle. A right angle is 90 degrees, by the way. So, if we do a little math magic, we can say that this angle is 90 + (90 * 0.5) degrees. That's 135 degrees, in case you're wondering.
Since we have an isosceles triangle, the two smaller angles are congruent. Now, if we take a look at the sum of the angles in a triangle, we know it's always 180 degrees. So, let's call those smaller angles x.
We have x + x + 135 = 180.
If we solve for x, we get x = (180 - 135) / 2. That's 22.5, my friend.
So, to sum it up (pun intended), each of the two smallest angles in this isosceles, obtuse triangle is approximately 22.5 degrees. Now, that's acute humor right there!
To solve this problem, let's start by finding the measure of a right angle.
The measure of a right angle is conventionally defined as 90 degrees. So, we can calculate 50% larger than a right angle by multiplying 90 by 1.5.
90 * 1.5 = 135
Therefore, one angle of the obtuse triangle has a measure of 135 degrees.
Now, an isosceles triangle has two congruent (equal) angles. Since we know one angle is 135 degrees, we can divide the remaining angle measure (360 - 135 = 225 degrees) by 2 to find the measure of each of the two smaller angles.
225 / 2 = 112.5
Hence, each of the two smallest angles in the triangle measures approximately 112.5 degrees.