Answer:
a = 107
Step-by-step explanation:
Given:
- One angle is 32°.
- Another angle is 75°.
- Angle is outside the triangle.
To solve for the size of the lettered angle in a right-angled triangle, we need to use the given angles and the properties of triangles.
- Identify the angles within the triangle
In a right-angled triangle, the sum of the angles is always 180°. Since one of the angles is 90°, the sum of the other two angles must be 90°.
Given angles = 32° + 75°
- Check the given angles
We notice that the sum of the given angles 32° + 75° = 107°, which is greater than 90°. This indicates that angle must be an exterior angle to the triangle.
- Determine the exterior angle
In any triangle, the exterior angle equals the sum of the two non-adjacent interior angles. Since is outside the triangle and we are given the sum of 32° and 75° is 107°, this sum corresponds to the exterior angle .
Therefore, the size of the angle is:
[tex]\boxed{a = 107^\circ}[/tex]
