Certainly! Let's answer each question step-by-step.
### Question 10:
What do you call the 2 coplanar angles that have a common side and a common vertex, but no common interior point?
- A. adjacent angles
- B. congruent angles
- C. supplementary angles
- D. complementary angles
Answer:
The correct answer is A. adjacent angles. Adjacent angles share a common side and a common vertex but do not overlap; hence, they have no common interior points.
### Question 11:
Which of the following angle pairs is always supplementary?
- A. adjacent angles
- B. vertical angles
- C. linear pair
- D. congruent angles
Answer:
The correct answer is C. linear pair. A linear pair consists of two adjacent angles whose non-common sides form a straight line, thus always summing to 180°, making them supplementary.
### Question 12:
What do you call coplanar lines that do not intersect?
- A. parallel lines
- B. intersecting lines
- C. perpendicular lines
- D. congruent lines
Answer:
The correct answer is A. parallel lines. Parallel lines are coplanar lines that do not meet, however far they are extended.
### Question 13:
Which of the following statements about an isosceles triangle is always true?
- A. It has two congruent sides.
- B. It is also an acute triangle.
- C. It is also a right triangle.
- D. It has one diagonal.
Answer:
The correct answer is A. It has two congruent sides. This is the defining property of an isosceles triangle - having exactly two sides of equal length.
### Question 14:
Which of the following descriptions about a quadrilateral is NOT true?
- A. It has 4 sides.
- B. It has 4 angles.
- C. It has 4 vertices.
- D. It has 4 diagonals
Answer:
The correct answer is D. It has 4 diagonals. A quadrilateral has only two diagonals, not four. The other three options correctly describe a quadrilateral.
### Question 15:
Which is the measure of each interior angle of a regular decagon?
- A. 80°
- C. 180°
- D. 360°
- B. 144°
Answer:
The correct answer is B. 144°. A regular decagon (a ten-sided polygon) has each interior angle measuring 144°. This can be derived using the formula for an interior angle of a regular polygon, [tex]\(\frac{(n-2) \times 180°}{n}\)[/tex].
Thus, the answers to the questions are as follows:
10. A
11. C
12. A
13. A
14. D
15. B
