https://file.aiquickdraw.com/mathbot/file/1727085746422u7f7aba3.jpg

The image shows two adjacent angles, labeled \( x - 28^\circ \) (acute angle) and \( x + 52^\circ \) (obtuse angle). These angles form a straight line, which means the sum of these angles should equal \( 180^\circ \).

The equation can be written as:
\[
(x - 28^\circ) + (x + 52^\circ) = 180^\circ
\]

Now, let's solve for \( x \).

\[
2x + 24^\circ = 180^\circ
\]
\[
2x = 180^\circ - 24^\circ
\]
\[
2x = 156^\circ
\]
\[
x = 78^\circ
\]

Now, to find the size of the obtuse angle \( x + 52^\circ \):
\[
x + 52^\circ = 78^\circ + 52^\circ = 130^\circ
\]

Thus, the size of the obtuse angle is \( 130^\circ \).

Would you like further details or have any questions?

Here are five related questions:
1. How do you determine if an angle is obtuse?
2. What is the relationship between supplementary angles?
3. How do adjacent angles add up to form a straight line?
4. What would happen if the given angles were complementary instead of supplementary?
5. Can angles greater than 180 degrees exist in Euclidean geometry?

**Tip**: Always check if angles are supplementary or complementary based on the given diagram to avoid calculation mistakes.

Calculate the size of the obtuse angle below. Give your answer in degrees (°). The angles provided are (x - 28)° and (x + 52)°.

Learn how to calculate the size of an obtuse angle using supplementary angles. The problem involves finding the angles (x - 28)° and (x + 52)° that add up to 180°. This solution covers key geometric concepts and is suitable for students in Grades 8-10.

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