Question : Three angles of a triangle are $(x-15^{\circ}),(x+45^{\circ}),$ and $(x+60^{\circ})$. Identify the type of triangle.

Option 1: Obtuse angle triangle

Option 2: Right angle triangle

Option 3: Isosceles triangle

Option 4: Equilateral triangle

Question : In $\triangle ABC$, AB = BC = $k$, AC =$\sqrt2k$, then $\triangle ABC$ is a:

Option 1: Isosceles triangle

Option 2: Right-angled triangle

Option 3: Equilateral triangle

Option 4: Right isosceles triangle

Question : ABC is an isosceles right-angled triangle with $\angle$B = 90°. On the sides AC and AB, two equilateral triangles ACD and ABE have been constructed. The ratio of the area of $\triangle$ABE and $\triangle$ACD is:

Option 1: $1 : 3$

Option 2: $2 : 3$

Option 3: $1 : 2$

Option 4: $1 : \sqrt{2}$

Question : In $\triangle$ABC, BD and CE are perpendicular to AC and AB respectively. If BD = CE, then $\triangle$ABC is:

Option 1: Equilateral

Option 2: Isosceles

Option 3: Right–angled

Option 4: Scalene

Question : One angle of an isosceles obtuse triangle is $28 \frac{1}{2}^{\circ}$. Find the measure of its obtuse angle in degrees.

Option 1: $132^{\circ}$

Option 2: $112^{\circ}$

Option 3: $121^{\circ}$

Option 4: $123^{\circ}$