https://r2.erweima.ai/mathbot/image/1726691633329n4wmpxpk.jpg

Let’s go through the math problems shown in the image step by step:

### Problem 1:
**"El suplemento de un ángulo equivale al triple de su complemento. Calcular el valor del ángulo."**

Let \( x \) be the angle. The complement of the angle is \( 90^\circ - x \), and the supplement is \( 180^\circ - x \).
The problem states:
\[
180^\circ - x = 3(90^\circ - x)
\]
Solve for \( x \):
\[
180^\circ - x = 270^\circ - 3x
\]
\[
2x = 90^\circ
\]
\[
x = 45^\circ
\]

### Problem 2:
**"El complemento del doble de un ángulo, aumentado en 148, equivale al suplemento del mismo."**

Let \( x \) be the angle. The complement of double the angle is \( 90^\circ - 2x \), and the supplement is \( 180^\circ - x \).
According to the problem:
\[
(90^\circ - 2x) + 148^\circ = 180^\circ - x
\]
Simplify:
\[
238^\circ - 2x = 180^\circ - x
\]
\[
x = 58^\circ
\]

### Problem 3:
**"Calcular \( x \), si \( OM \) es bisectriz del ángulo \( AOB \)."**

Given that \( OM \) bisects the angle \( AOB \), we know:
\[
\angle AOM = \angle MOB
\]
Since \( \angle AOB = 20^\circ + 10^\circ = 30^\circ \), the bisected angles are:
\[
x = \frac{30^\circ}{2} = 15^\circ
\]

### Problem 4:
**"Calcular \( x \)."**

This is a linear pair, where the angles are supplementary:
\[
30^\circ + x = 2x + 25^\circ
\]
Solve for \( x \):
\[
30^\circ - 25^\circ = x
\]
\[
x = 5^\circ
\]

### Problem 5:
**"Calcular \( x \)."**

We have two angles: \( 130^\circ \) and \( x \). They form a linear pair, meaning:
\[
x + 130^\circ = 180^\circ
\]
Solve for \( x \):
\[
x = 50^\circ
\]

Would you like details on other problems or more explanations?

### Related Questions:
1. How can you find the complement of an angle?
2. What is the difference between complementary and supplementary angles?
3. What is an angle bisector, and how is it used in geometry?
4. How do you solve for unknowns in equations involving angles?
5. How do linear pairs of angles help in solving geometry problems?

### Tip:
When solving geometry problems, it's helpful to draw or visualize the angles to better understand their relationships.

Solve a set of geometry problems involving angle complements, supplements, and bisectors.

Solve a variety of geometry problems involving angle complements, supplements, and bisectors. This includes step-by-step solutions using key geometric formulas and theorems suitable for Grades 7-9.

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