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Hey there!
The interior angles of a triangle always have to add up to 180 degrees.
We are told that this is a right triangle, so one of the angles must be 90 degrees. This means that the measures of the other two angles must add up to 90.
90 + m<1 + m<2 = 180
If the smallest angle is 45 degrees less than the next largest angle, the only option for this would be for both of the remaining angles to be 45 degrees. The next largest angle would be the right angle, and 90 - 45 = 45.
We can't have any of the other angles be more than 90 degrees because then it wouldn't be a proper triangle.
So, the measures of the angles are going to be 90, 45, and 45.
Hope this helps!
The measurement of the smallest angle in a right triangle is 45° less than the measure of the next larger angle. The three angle of right are ( [tex]90^o, 45^o, 45^o[/tex] )
What is right angle triangle property?
In a right angle triangle, the largest angle is equal to the 90 degrees, and the some of the other two angle is equal to the 90 degrees.
Given information-
The smallest angle in a right triangle is 45° less than the measure of the larger angle.
Suppose the smallest angle of the right triangle is x degrees.
Now as the smallest angle in a right triangle is 45° less than the measure of the larger angle and the value of largest angle is 90 degrees in the right angle triangle. Thus,
[tex]x=90-45\\x=45^o[/tex]
Hence, the measurement of the smallest angle is 45 degrees.
Let the other angle of the right angle triangle is y degrees.
As the some of the all the angles of a triangle is equal the 180 degrees. Thus,
[tex]x+y+90=180\\45+y=180-90\\y=90-45\\y=45[/tex]
Thus, the measurement of the other angle is 45 degrees.
Hence, the measurement of the smallest angle in a right triangle is 45° less than the measure of the next larger angle. The three angle of right are ( [tex]90^o, 45^o, 45^o[/tex] )
Learn more about the right angle triangle property here;
https://brainly.com/question/22790996
