The image presents a triangle $\triangle DEF$ with two equal sides (an isosceles triangle). The angle $\angle E$ is given as $74^\circ$, and the angle $\angle D$ is marked as $x^\circ$.

To find $x$:

• In any triangle, the sum of the interior angles is always $180^\circ$.
• Since $\triangle DEF$ is isosceles, the base angles $\angle D$ and $\angle F$ are equal. Hence, $x = \angle F$.

Let’s denote the angles as: $\angle D + \angle E + \angle F = 180^\circ$ $x + 74^\circ + x = 180^\circ$ This simplifies to: $2x + 74^\circ = 180^\circ$ Subtract $74^\circ$ from both sides: $2x = 106^\circ$ Now, divide by 2: $x = 53^\circ$

Therefore, the value of $x$ is $53^\circ$.

Would you like further details on how this was calculated, or do you have any questions?

Here are 5 related questions you can explore:

1. How do you calculate the angles in a right triangle?
2. What makes an isosceles triangle different from a scalene triangle?
3. How can you determine the area of an isosceles triangle if the base and height are known?
4. What is the exterior angle theorem for triangles, and how does it apply to this problem?
5. How do the properties of equilateral triangles differ from those of isosceles triangles?

Tip: Always remember that the sum of interior angles in any triangle is $180^\circ$. This is a fundamental property that helps in solving angle problems in triangles.