Answer:
82°
Explanation:
You want the unmarked remote interior angle of a triangle, given that one of them is 61°, and the exterior angle opposite is 143°.
Interior angles
The exterior angle is the sum of the remote interior angles:
143° = 61° +∠B
∠B = 143° -61° . . . . subtract 61°
∠B = 82°
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Additional comment
In case you don't remember the remote interior angles theorem, you can get the same result using angle relations you do remember:
- the sum of angles in a triangle is 180°
- a linear pair totals 180°
The interior angle at A is the supplement of the exterior angle:
∠A = 180° -143°
When ∠A is added to the other two interior angles, the total is 180°:
∠A +∠B +61° = 180°
(180° -143°) +∠B +61° = 180° . . . . . . use the above expression for ∠A
Rearranging this to give the value of angle B, we have ...
∠B = 180° -180° +143° -61°
∠B = 143° -61° = 82° . . . . . . as above
Another way to get there is to consider ...
The sum of ∠B and 61° is supplementary to interior angle A (their total is 180°). The exterior angle 143° is supplementary to interior angle A. Two angles supplementary to the same angle are equal, so the sum of ∠B and 61° is equal to the exterior angle 143°.