Answer:
A = 48°
B = 66°
C = 66°
D = 20°
E = 20°
F = 160°
G = 160°
Step-by-step explanation:
Angle A
According to the Triangle Sum Theorem, the sum of the interior angles in any triangle is always equal to 180°. Therefore:
A + 90° + 42° = 180°
A + 132° = 180°
A + 132° - 132° = 180° - 132°
A = 48°
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Angle B
Angles on a straight line sum to 180°, so:
A + B + C = 180°
48° + B + C = 180°
Given that B = C, then:
48° + B + B = 180°
48° + 2B = 180°
48° + 2B - 48° = 180° - 48°
2B = 132°
B = 66°
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Angle C
As angle B is congruent to angle C, then C = B.
Since B = 66°, then:
C = 66°
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Angle D
According to the Triangle Sum Theorem, the sum of the interior angles in any triangle is always equal to 180°. Therefore:
94° + C + D = 180°
94° + 66° + D = 180°
160° + D = 180°
160° + D - 160° = 180° - 160°
D = 20°
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Angle E
The Vertical Angles Theorem states that when two lines intersect, the pairs of vertical angles formed are congruent. Since angles E and D are vertical, and D = 20°, then:
E = D
E = 20°
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Angle F
Angles F and D form a linear pair, so the sum of their measures is always 180°. Therefore:
F + D = 180°
F + 20° = 180°
F + 20° - 20° = 180° - 20°
F = 160°
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Angle G
The Vertical Angles Theorem states that when two lines intersect, the pairs of vertical angles formed are congruent. Since angles G and F are vertical, and F = 160°, then:
G = F
G = 160°
