Diagram of two connected triangles with labeled angles involving variables y and 68°.

Let’s solve this step by step.

We are given a quadrilateral with points A, B, C, D. There’s a right angle at point C (marked with the square symbol). Also, there’s an exterior angle of 68° at point A, and two angles labeled in terms of y: one is 2y at point B, and another is y + 48° at point D (this is an exterior angle).

First, let’s find the interior angle at point A.

The 68° angle shown is outside the shape — it’s adjacent to the interior angle at A. Since they form a straight line, they add up to 180°.

So, interior angle at A = 180° - 68° = 112°

Now, look at point D. The angle marked as y + 48° is also an exterior angle. That means the interior angle at D is:

Interior angle at D = 180° - (y + 48°) = 132° - y

At point C, we have a right angle → that’s 90°.

At point B, the interior angle is given as 2y.

Now, remember: the sum of all interior angles in any quadrilateral is always 360°.

So, let’s write the equation:

Angle A + Angle B + Angle C + Angle D = 360°

Plug in what we know:

112° + 2y + 90° + (132° - y) = 360°

Now simplify:

Combine constants: 112 + 90 + 132 = 334

Combine y terms: 2y - y = y

So:

334 + y = 360

Subtract 334 from both sides:

y = 360 - 334 = 26

✔ Let’s double-check:

If y = 26,

- Angle at B = 2y = 52°
- Exterior angle at D = y + 48 = 74° → so interior angle at D = 180 - 74 = 106°
- Angle at A = 112° (as calculated)
- Angle at C = 90°

Sum: 112 + 52 + 90 + 106 = 360° → Correct!

Final Answer:
26