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? [1] 30 and 30 [ 2] 30 and 60 [ 3] 45 and 45 [ 4] 60 and 60 [5] 45 and 30
the answer is 3
180 - (90/2) = ?
To find the measures of the two remaining angles in a triangle, we need to use the fact that the sum of all angles in a triangle is always 180 degrees.
Given that one angle of the triangle is 90 degrees, and the ratio of the legs is 1:1, we can determine the measures of the other two angles.
Let's call the two remaining angles A and B.
Since one angle is 90 degrees, we have:
A + B + 90 = 180
Subtracting 90 from both sides, we get:
A + B = 90
Since the legs of the triangle have a ratio of 1:1, the two remaining angles will be equal.
If we represent the measure of each of these angles as x, we have:
A = x and B = x
Substituting these values into the equation A + B = 90, we get:
x + x = 90
2x = 90
Dividing both sides by 2, we find:
x = 45
Therefore, the two remaining angles in the triangle are both 45 degrees.
So the correct answer is option [3] 45 and 45.
To find the measures of the two remaining angles in a triangle, we need to use the fact that the sum of the angles in a triangle is always 180 degrees.
Given that one angle of the triangle is 90 degrees, we know that the other two angles must add up to 180 - 90 = 90 degrees.
Since the ratio of the legs is 1:1, we can conclude that the two remaining angles are congruent (have the same measure). Let's call this measure x.
So, we have the equation: x + x = 90.
Simplifying the equation, we get: 2x = 90.
To solve for x, we divide both sides of the equation by 2: x = 45.
Therefore, the measures of the two remaining angles are both 45 degrees.
Hence, the correct answer is [3] 45 and 45.