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Question 1: What is the sum of the angles in a linear pair?
Solution: The sum of angles in a linear pair is $180^\circ$.
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Question 2: Find the complement of an angle of $65^\circ$.
Solution: Complement $= 90^\circ - 65^\circ = 25^\circ$.
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Question 3: If two lines intersect each other, what is the relation between vertically opposite angles?
Solution: Vertically opposite angles are equal.
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Question 4: An angle is greater than $90^\circ$ and less than $180^\circ$. What type of angle is it?
Solution: It is an Obtuse angle.
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Question 5: In $\triangle ABC$, if $\angle A = 50^\circ$ and $\angle B = 60^\circ$, find $\angle C$.
Solution: $\angle A + \angle B + \angle C = 180^\circ$ (Angle sum property).
$50^\circ + 60^\circ + \angle C = 180^\circ \Rightarrow 110^\circ + \angle C = 180^\circ \Rightarrow \angle C = 70^\circ$. -
Question 6: Find the supplement of $110^\circ$.
Solution: Supplement $= 180^\circ - 110^\circ = 70^\circ$.
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Question 7: If a transversal intersects two parallel lines, then consecutive interior angles are?
Solution: Consecutive interior angles (or co-interior angles) are supplementary (sum is $180^\circ$).
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Question 8: What is the measure of a complete angle?
Solution: A complete angle measures $360^\circ$.
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Question 9: Can a triangle have two right angles?
Solution: No, because the sum of two right angles is $180^\circ$, leaving $0^\circ$ for the third angle, which is not possible.
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Question 10: If one angle of a linear pair is acute, then what kind of angle is the other?
Solution: The other angle must be obtuse (since sum is $180^\circ$).