One of the angles of △MNO has a measure of 37°. One of the angles of △UVW has a measure of 53°. If △MNO and △UVW are similar, what is the measure of the largest angle of △MNO?
Question
One of the angles of △MNO has a measure of 37°. One of the angles of △UVW has a measure of 53°. If △MNO and △UVW are similar, what is the measure of the largest angle of △MNO?
Solution
The largest angle in a triangle is always opposite the longest side. However, in this problem, we are not given any information about the sides of the triangles. We are only given information about the angles.
In similar triangles, corresponding angles are equal. This means that if one angle in △MNO is 37°, then there is an angle in △UVW that is also 37°. Similarly, if one angle in △UVW is 53°, then there is an angle in △MNO that is also 53°.
The sum of the angles in a triangle is always 180°. So, to find the measure of the largest angle in △MNO, we can subtract the measures of the two known angles from 180°.
180° - 37° - 53° = 90°
So, the measure of the largest angle in △MNO is 90°.
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