In a triangle, the sum of all three angles is always 180°. Given that one angle measures 90°, we can find the measures of the other two angles. Let's call the first angle x. The other two angles are in a ratio of 4:5. This means that the second angle is 4 times smaller than the third angle. So, the second angle is 4x and the third angle is 5x. Since the sum of all three angles in a triangle is 180°, we can write the equation: x + 4x + 5x = 180 Combining like terms: 10x = 180 To solve for x, we divide both sides of the equation by 10: 10x/10 = 180/10 x = 18 Now, we can find the measures of the other two angles: Second angle = 4x = 4 * 18 = 72° Third angle = 5x = 5 * 18 = 90° Therefore, the measures of the two angles in the triangle, other than the 90° angle, are 72° and 90°.
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