Question: MATHEMATICS EXERCISE SET 2-3 : GEOMETRY AND TRIGONOMETRY
MATHEMATICS EXERCISE SET 2-3 : GEOMETRY AND TRIGONOMETRY
Read and answer each of the questions carefully. Choose the letter corresponding to your answer and
shade the letter corresponding to your choice.
Do not use a calculator in answering these questions.
1. What is the value of an angle if 100° less than two times its supplement is thrice
its complement?
A. 2°
B. 10°
C. 20°
D. 90°
1. **Problem:** Find the value of an angle $x$ such that $100$ less than two times its supplement equals thrice its complement.
2. **Recall definitions:**
- Supplement of $x$ is $180^\circ - x$.
- Complement of $x$ is $90^\circ - x$.
3. **Set up the equation:**
Two times supplement minus 100 equals thrice complement:
$$2(180 - x) - 100 = 3(90 - x)$$
4. **Expand and simplify:**
$$360 - 2x - 100 = 270 - 3x$$
$$260 - 2x = 270 - 3x$$
5. **Isolate $x$:**
Add $3x$ to both sides:
$$260 - 2x + 3x = 270$$
$$260 + x = 270$$
6. **Solve for $x$:**
$$x = 270 - 260 = 10$$
7. **Answer:** The value of the angle is $10^\circ$.
**Final answer:** B. 10°