9514 1404 393
Answer:
(a) (2x +36)° +(3x +14)° = 90°
(b) ∠C = 38°; ∠D = 52°; ∠E = 90°
Explanation:
(a) Two acute angles are marked in a right triangle. We know the sum of angles in a triangle is 180°, so if one of those angles is 90°, the sum of the other two angles must be 90°. We can use that fact to write and equation for x.
(2x +36)° +(3x +14)° = 90°
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(b) We can collect terms, subtract 50 and ...
5x +50 = 90 . . . . . . . collect terms, divide by °
5x = 40 . . . . . . . . . . subtract 50
x = 8 . . . . . . . . . .. divide by 5
∠C = (3x +14)° = (3·8 +14)° = 38°
∠D = (2x +36)° = (2·8 +36)° = 52°
∠E = 90°
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Angle E is marked as a right angle by the little square in that corner. The measure of a right angle is 90°, by definition.