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Hint

1

**Acute Angle**

Less than 90 degrees

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2

**Right Angle**

Exactly 90 degrees

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3

**Obtuse Angle**

Greater than 90 degrees but less than 180 degrees

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4

**Straight Angle**

Exactly 180 degrees

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5

**Complementary Angles**

Two angles that add up to 90 degrees

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6

**Supplementary Angles**

Two angles that add up to 180 degrees

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7

**Adjacent Angles**

Two angles that share a common side and vertex

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8

**Vertical Angles**

Opposite angles formed by two intersecting lines; they are always equal

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9

**Corresponding Angles**

Angles in the same relative position at each intersection; they are equal

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10

**Alternate Interior Angles**

Angles on opposite sides of the transversal but inside the parallel lines; they are equal

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11

**Alternate Exterior Angles**

Angles on opposite sides of the transversal but outside the parallel lines; they are equal

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12

**Consecutive Interior Angles**

Angles on the same side of the transversal and inside the parallel lines; they add up to 180 degrees

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13

**Triangle Angle Sum**

The sum of the interior angles of a triangle is always 180 degrees.

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14

**Angle Sum Theorem**

The sum of the interior angles of a triangle is 180 degrees: ( angle A + angle B + angle C = 180).

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15

**Exterior Angle Theorem**

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles.

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16

**Parallel Lines and Transversals**

Corresponding angles are equal: ( angle 1 = angle 5 )

Alternate interior angles are equal: ( angle 3 = angle 6 )

Alternate exterior angles are equal: ( angle 2 = angle 7 )

Consecutive interior angles are supplementary: ( angle 4 + angle 6 = 180^)

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17

If ( angle A = 30^), find its complement and supplement.

Complement: ( 90^ - 30^ = 60^)

Supplement: ( 180^ - 30^ = 150^)

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18

If two intersecting lines form angles such that one angle is 40^, find the measures of all angles.

Vertical angles: ( 40^) and ( 40^)

Adjacent angles: ( 140^) and ( 140^)

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19

If two parallel lines are cut by a transversal and one of the alternate interior angles is 85^, find all the other angles.

Alternate interior angle: ( 85^)

Corresponding angle: ( 85^)

Consecutive interior angle: ( 180^- 85^= 95^)

Alternate exterior angle: ( 85^)

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20

In triangle ABC, if ( angle A = 50^) and ( angle B = 60^), find ( angle C ).

( angle C = 180^ - angle A - angle B )

( angle C = 180^ - 50^- 60^ = 70^)

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21

In triangle DEF, if the exterior angle at vertex E is ( 120^) and the interior opposite angles are ( angle D = 70^) and ( angle F = x ), find ( x ).

( 120^ = 70^ + x )

( x = 120^ - 70^= 50^)

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