By analyzing the angles in the smaller triangle and using the principle of complementary angles in a right triangle, we found that x = 10° and y = 80°.
Note: If the angle in the smaller triangle is indeed -10°, then the problem statement or image might contain an error. Please double-check the information provided.
Identify usable angles: We know the angles of the smaller triangle: 100° and 90° (right angle).
Sum of angles in a triangle: The sum of angles in any triangle is 180°. Therefore, in the smaller triangle:
x° + 100° + 90° = 180°
x° = 180° - 100° - 90°
x° = -10° (This is not a valid angle measure for a triangle. Check for errors in the image or problem statement.)
Complementary angles: In a right triangle, the two acute angles are complementary, meaning they add up to 90°. Therefore:
x° + y° = 90°
Substitute and solve for y: Since x° is negative, we need to re-evaluate the angle information. Assuming the intended angle for the smaller triangle is 10° (not -10°), we can substitute and solve for y:
10° + y° = 90°
y° = 90° - 10°
y° = 80°
Therefore:
x = 10°
y = 80°