Question: 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
is complement?
A. 2°
B. 10°
C. 20°
D. 90°
1. **Problem:** Find the value of an angle $x$ such that $100$ degrees less than two times its supplement equals thrice its complement.
2. **Step 1: Define the supplement and complement of $x$.**
- Supplement of $x$ is $180^\circ - x$.
- Complement of $x$ is $90^\circ - x$.
3. **Step 2: Translate the problem into an equation.**
Two times the supplement minus $100$ equals three times the complement:
$$2(180 - x) - 100 = 3(90 - x)$$
4. **Step 3: Simplify both sides.**
$$360 - 2x - 100 = 270 - 3x$$
$$260 - 2x = 270 - 3x$$
5. **Step 4: Solve for $x$.**
Add $3x$ to both sides:
$$260 - 2x + 3x = 270$$
$$260 + x = 270$$
Subtract $260$ from both sides:
$$x = 270 - 260$$
$$x = 10$$
6. **Step 5: Conclusion.**
The value of the angle is $10^\circ$.
**Answer: B. 10°**