1. **Problem:** In triangle ABC, given that $\angle A = \angle B = 62^\circ$, find $\angle C$. 2. **Formula:** The sum of the interior angles of any triangle is always $180^\circ$. That is, $$\angle A + \angle B + \angle C = 180^\circ$$ 3. **Calculation:** Substitute the known values: $$62^\circ + 62^\circ + \angle C = 180^\circ$$ 4. Simplify the left side: $$124^\circ + \angle C = 180^\circ$$ 5. Solve for $\angle C$: $$\angle C = 180^\circ - 124^\circ = 56^\circ$$ 6. **Answer:** $\angle C = 56^\circ$. --- 1. **Problem:** Find the area of a triangle with angles $72^\circ$, $29^\circ$, and $29^\circ$. 2. **Note:** To find the area, we need side lengths or height, but since only angles are given, we can classify the triangle or find relative side lengths using the Law of Sines if a side is known. Since no side is given, we cannot find the exact area. 3. **Classification:** Since two angles are equal ($29^\circ$), the triangle is isosceles. --- 1. **Problem:** Classify the triangles according to their angles. (a) Triangle PQR with angles $120^\circ$, $30^\circ$, $30^\circ$. - Since one angle is greater than $90^\circ$, it is an obtuse triangle. (b) Triangle MNL with angles $90^\circ$, $60^\circ$, $30^\circ$. - Since one angle is exactly $90^\circ$, it is a right triangle. --- 1. **Problem:** Choose the correct answers for the following: (a) The angles of a triangle are in the ratio 2:3:4. Find the largest angle. 2. **Calculation:** Let the common ratio be $x$. Then angles are $2x, 3x, 4x$. Sum of angles: $$2x + 3x + 4x = 9x = 180^\circ$$ Solve for $x$: $$x = \frac{180^\circ}{9} = 20^\circ$$ Largest angle: $$4x = 4 \times 20^\circ = 80^\circ$$ Answer: (c) 80° --- (b) The largest angle is: From above, largest angle is $80^\circ$, but options are 60°, 120°, 100°. None matches 80°, so the correct largest angle from the options is not listed. Possibly a typo. --- (c) The angles of a triangle are 50°, 70°, and $x^\circ$. Find $x$. Sum of angles: $$50^\circ + 70^\circ + x = 180^\circ$$ Solve for $x$: $$x = 180^\circ - 120^\circ = 60^\circ$$ Answer: (a) 60° --- **Summary:** - $\angle C = 56^\circ$ in triangle ABC. - Triangle with angles 72°, 29°, 29° is isosceles. - Triangle PQR is obtuse. - Triangle MNL is right angled. - Largest angle in ratio 2:3:4 is 80°. - Missing angle in 50°, 70°, $x$ triangle is 60°.