10 questions · Form 1 Mathematics Bab 8: Lines and Angles
Which basic angle is created first when constructing standard geometric angles using only compasses and a ruler?
Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.
1. Which basic angle is created first when constructing standard geometric angles using only compasses and a ruler?
Answer: C
A 60° angle is constructed by making intersecting arcs of equal radius (forming the base of an equilateral triangle).
2. Four angles surrounding a point are 2x°, 3x°, 100°, and 110°. Find the value of x.
Answer: A
Sum of angles at a point = 360°. 2x + 3x + 100 + 110 = 360 => 5x + 210 = 360 => 5x = 150 => x = 30.
3. Given two parallel lines intersected by a transversal, if an alternate angle pair is (x + 20)° and 75°, find x.
Answer: A
Alternate angles are equal: x + 20 = 75 => x = 55.
4. If angle x and angle y are complementary angles, and x = 35°, what is the value of y?
Answer: A
Complementary angles add up to 90°. Therefore, y = 90° - 35° = 55°.
5. What is the measure of each angle formed when a perpendicular bisector intersects a line segment?
Answer: C
By definition, 'perpendicular' means intersecting at right angles (90°).
6. What is the conjugate angle of 140°?
Answer: C
Conjugate angles add up to 360°. Conjugate angle = 360° - 140° = 220°.
7. If line AB is parallel to line CD, and a transversal forms corresponding angles of 3y° and 105°, find y.
Answer: A
Corresponding angles are equal: 3y = 105 => y = 35.
8. If the angle of elevation of a kite from a person standing on the ground is 42°, what is the angle of depression of the person from the kite?
Answer: C
The angle of elevation from point A to point B is equal to the angle of depression from point B to point A due to alternate interior angles.
9. Two straight lines intersect at a point. If one angle is 125°, what is the measure of its vertically opposite angle?
Answer: B
Vertically opposite angles formed by intersecting lines are equal, so the angle is 125°.
10. If angle A and angle B are supplementary, and angle A is twice the measure of angle B, find the measure of angle B.
Answer: B
A + B = 180°. Given A = 2B, so 2B + B = 180 => 3B = 180 => B = 60°.