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
i need your help please guys thanks
To find the measures of the two remaining angles, we can utilize the fact that the sum of all angles in a triangle is always equal to 180 degrees.
Since one angle of the triangle is 90 degrees, we have 180 - 90 = 90 degrees remaining for the other two angles.
Given that the ratio of the legs is 1:1, we can conclude that the two remaining angles must be equal. Let's represent the measures of these angles as x.
Now, we have:
x + x + 90 = 180
By combining like terms, we get:
2x + 90 = 180
Subtracting 90 from both sides we have:
2x = 180 - 90
2x = 90
Dividing both sides by 2:
x = 45
Therefore, the two remaining angles in the triangle are 45 degrees each.
Hence, the correct answer is option [3] 45 and 45.
To find the measures of the two remaining angles in a right triangle when one angle is 90 degrees and the ratio of the legs is 1:1, we can use the fact that the sum of the angles in a triangle is always 180 degrees.
Let's denote the two remaining angles as A and B.
Since one angle is 90 degrees, the sum of the other two angles must be 180 - 90 = 90 degrees.
If the ratio of the legs in the triangle is 1:1, it means that the two remaining sides are equal in length. Therefore, the two remaining angles must also be equal.
Since the sum of two equal angles is 90 degrees, we can divide 90 by 2 to find each angle measure.
90 / 2 = 45
Therefore, the two remaining angles in the triangle are both 45 degrees.
Thus, the correct answer is: [3] 45 and 45