Q1. If one angle of a triangle is 90 degrees and the other two angles are equal, what are the measures of the other two angles?
Solution:
In a triangle, the sum of the angles is 180 degrees. If one angle is 90 degrees, the remaining two angles must sum to 90 degrees. Since they are equal, each must be 45 degrees.
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Q2. If a quadrilateral has two pairs of opposite sides that are equal, what type of quadrilateral is it?
Solution:
A quadrilateral with two pairs of opposite sides that are equal is classified as a parallelogram.
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Q3. In a triangle, if one angle measures 30 degrees and the other measures 60 degrees, what is the measure of the third angle?
Solution:
The third angle can be found by subtracting the sum of the other two angles from 180 degrees: 180 - (30 + 60) = 90 degrees.
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Q4. In a right triangle, if one leg measures 6 cm and the other leg measures 8 cm, what is the length of the hypotenuse?
Solution:
Using the Pythagorean theorem, c² = a² + b². Here, c² = 6² + 8² = 36 + 64 = 100, so c = √100 = 10 cm.
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Q5. In a parallelogram, if one angle measures 70 degrees, what are the measures of the other three angles?
Solution:
In a parallelogram, opposite angles are equal and adjacent angles are supplementary. Therefore, if one angle is 70 degrees, the opposite angle is also 70 degrees, and the adjacent angles are 110 degrees each.
