Question

Which of the following are ways of constructing an angle of 105${}^{\circ }$ using the two types of set squares?

• A. 125${}^{\circ }$ - 20${}^{\circ }$
• B. 60${}^{\circ }$ + 45${}^{\circ }$
• C. 90${}^{\circ }$ + 45${}^{\circ }$ - 30${}^{\circ }$
• D. 30${}^{\circ }$ + 30${}^{\circ }$ + 45${}^{\circ }$

Answer 1

Answer: (B), (C), (D)

The correct options are
B

60${}^{\circ }$ + 45${}^{\circ }$

C

90${}^{\circ }$ + 45${}^{\circ }$ - 30${}^{\circ }$

D

30${}^{\circ }$ + 30${}^{\circ }$ + 45${}^{\circ }$

Given two different types of set squares ( 30-60-90 and 45-45-90 ), we have four different angles to play with: 30${}^{\circ }$, 45${}^{\circ }$, 60${}^{\circ }$ and 90${}^{\circ }$.

Note that,
${30}^{\circ }+{30}^{\circ }+{45}^{\circ }={60}^{\circ }+{45}^{\circ }={90}^{\circ }+{45}^{\circ }-{30}^{\circ }={105}^{\circ }$

Also, 125${}^{\circ }$ is an angle that cannot be constructed even by using both the set squares. Thus, option (a) is incorrect.