One angle of a triangle is 90 degrees.If the ratio of the legs is 1:1 what are the measures (in degrees) of the two remaining angles?
45 + 45 + 90 = 180
opposite sides equal -->isoceles --> opposite angles equal and they sum to 90
45
45 and 45
45
i got it!....thank you appreciate it! xo
Well, well, well, we've got ourselves a right triangle! How exciting! Now, since one angle is already 90 degrees, we only need to find the measures of the other two angles.
In a right triangle, the sum of the measures of the other two angles is always 90 degrees. Since the ratio of the legs is 1:1, that means both of these angles will be equal.
So, let's call each of these angles "x." We know that x + x = 90 degrees.
Simplifying that equation, we have:
2x = 90
Now, to find x, divide both sides of the equation by 2:
x = 45
So, the measures of the two remaining angles in your triangle are both 45 degrees. It seems symmetry is playing its role here!
To find the measures of the two remaining angles in a triangle with one angle of 90 degrees and legs in a 1:1 ratio, we can use the fact that the sum of the angles in a triangle is always equal to 180 degrees.
In this case, we already know that one angle is 90 degrees. Let's call the other two angles A and B.
Since the sum of the angles in a triangle is 180 degrees, we can write the equation:
90 + A + B = 180
To find the measures of angles A and B, we need one more piece of information. The ratio of the legs being 1:1 implies that the other two sides of the triangle are congruent (equal in length). Therefore, the remaining angles are also congruent.
Let's assume that the measures of angles A and B are equal. We can represent this using the variable x:
A = B = x
Now, we can substitute these values into the equation we wrote earlier:
90 + x + x = 180
Combine like terms:
90 + 2x = 180
Subtract 90 from both sides:
2x = 90
Divide by 2:
x = 45
So, each of the remaining angles A and B is equal to 45 degrees.
Therefore, the measures of the two remaining angles in the triangle are both 45 degrees.