Two angles form a linear pair. One angle measures four times the other. Find the two angles

Let the measure of the smaller angle be \( x \). Since the two angles form a linear pair, their sum is \( 180^\circ \). Also, we are given that one angle is four times the other, so the larger angle will be \( 4x \).

The equation for the sum of the angles is:

\[
x + 4x = 180^\circ
\]

Simplifying:

\[
5x = 180^\circ
\]

\[
x = \frac{180^\circ}{5} = 36^\circ
\]

Now, the measure of the other angle is:

\[
4x = 4 \times 36^\circ = 144^\circ
\]

Thus, the two angles are \( 36^\circ \) and \( 144^\circ \).

Would you like more details or have any questions?

Here are 5 related questions:
1. What are complementary angles, and how are they different from a linear pair?
2. Can two obtuse angles form a linear pair?
3. How do you calculate angles that are supplementary but not a linear pair?
4. What is the relationship between vertically opposite angles?
5. If one angle is twice another in a linear pair, what are the two angles?

**Tip:** A linear pair always sums to 180°, which means the two angles are supplementary.

Two angles form a linear pair. One angle measures four times the other. Find the two angles.

Learn how to solve the problem where two angles form a linear pair, and one measures four times the other. The solution involves using the linear pair and supplementary angles theorems, and is suitable for students in Grades 6-8.

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