A right triangle has acute angles measuring 3X degrees and 2X +10° use the triangle angle sum theorem to find the measures of the missing angles of the triangle
To find the measures of the missing angles, we first need to determine the measure of the third angle in the triangle.
According to the Triangle Angle Sum Theorem, the sum of the three angles in any triangle is always 180 degrees.
So, we have:
3X + 2X + 10 + Third angle = 180°
5X + 10 + Third angle = 180°
Now, we know that two angles in the triangle have measures of 3X and 2X + 10 degrees, so the third angle is given by:
Third angle = 180° - (3X + 2X + 10)
Third angle = 180° - (5X + 10)
Third angle = 180° - 5X - 10
Third angle = 170° - 5X
Now we know the measure of the third angle in the triangle; we can substitute the given expressions for the other two angles and solve for X.
3X = 3(30) = 90
2X + 10 = 2(30) + 10 = 60 + 10 = 70
Third angle = 170 - 5(30) = 170 - 150 = 20
Therefore, the measures of the angles in the triangle are 90°, 70°, and 20°.