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32°
75°
a
hello,pls help me find the sizes of the lettered angle,and Reason,it is a right angle triangle where a is outside the triangle​

Sagot :

chibabykalu16

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.

  1. 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°
  2. 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.
  3. 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]

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