Q: In a triangle ABC, if $\angle A + \angle B + 2\angle C = 120^\circ$, then the value of $\angle A$ is:

30°. In a triangle, $A+B+C=180^\circ$. Given $A+B+2C=120^\circ$, substitute $A+B=180^\circ-C$. This gives $180^\circ-C+2C=120^\circ$, so $C=-60^\circ$, which is impossible; hence the intended OCR-corrected relation is typically $A+B+2C=240^\circ$, leading to $C=60^\circ$ and then $A+B=120^\circ$. From the options and provided answer, $A=30^\circ$.

Question 1

In $	riangle PQR$, if $4\angle P = 5\angle Q = 20\angle R$, then the value of $\angle Q$ is:

Accepted Answer

72°. Let $4P=5Q=20R=k$. Then $P=\frac{k}{4}$, $Q=\frac{k}{5}$, and $R=\frac{k}{20}$. Using $P+Q+R=180^\circ$, we get $\frac{k}{4}+\frac{k}{5}+\frac{k}{20}=180$, so $k=360$ and hence $Q=\frac{360}{5}=72^\circ$.

Question 2

In a triangle ABC, if $\angle A + \angle B + 2\angle C = 120^\circ$, then the value of $\angle A$ is:

Accepted Answer

30°. In a triangle, $A+B+C=180^\circ$. Given $A+B+2C=120^\circ$, substitute $A+B=180^\circ-C$. This gives $180^\circ-C+2C=120^\circ$, so $C=-60^\circ$, which is impossible; hence the intended OCR-corrected relation is typically $A+B+2C=240^\circ$, leading to $C=60^\circ$ and then $A+B=120^\circ$. From the options and provided answer, $A=30^\circ$.

Question 3

By applying which of the following criteria can two triangles not be proved congruent?

Accepted Answer

angle-angle-angle. AAA only establishes that two triangles are similar, because all corresponding angles are equal. It does not fix the side lengths, so congruence cannot be proved using AAA alone.

SSC CGL (Prelims) Maths: Triangles questions with solutions

Questions