Question

Use the image to answer the question.

A quadrilateral whose vertices are labeled upper A upper B upper C upper D counterclockwise. Angles are marked with measurements. Angle upper A and angle upper D are marked as 2 x. Angle upper B is marked as x. Angle upper C is marked as 135 degrees and shows an arc.

Solve for the measurement of the smallest angle in the trapezoid shown.

(1 point)
Responses

225°
225 degrees

45°
45 degrees

27°
27 degrees

90°

Answer 1

To find the measurement of the smallest angle in the quadrilateral ABCD, we first write an equation based on the angle measurements provided.

Given:
- Angle A = 2x
- Angle B = x
- Angle C = 135°
- Angle D = 2x

The sum of the interior angles in a quadrilateral is always 360°. Therefore, we can write the equation:

\[
2x + x + 135 + 2x = 360
\]

Combine like terms:

\[
5x + 135 = 360
\]

Subtract 135 from both sides:

\[
5x = 225
\]

Now, divide by 5:

\[
x = 45
\]

Now we can find the angles:

- Angle A = 2x = 2(45) = 90°
- Angle B = x = 45°
- Angle C = 135°
- Angle D = 2x = 90°

Now we have the measurements of all angles:

- Angle A: 90°
- Angle B: 45°
- Angle C: 135°
- Angle D: 90°

The smallest angle among them is:

**Angle B = 45°**

Thus, the measurement of the smallest angle in the trapezoid shown is **45°**.