In a diagram below the larger angles is four times bigger than the smaller angle find the two unknown angles.

Let the smaller angle be $x$.
Let the larger angle be $y$.

The problem states that the larger angle is four times bigger than the smaller angle:

The diagram shows two angles on a straight line, which means they are supplementary. Their sum is $180^\circ$:

Substitute $y = 4x$ into $x + y = 180^\circ$:

Combine like terms:

Divide by 5:

Use the relationship $y = 4x$:

The two unknown angles are $36^\circ$ and $144^\circ$.

The smaller angle is $\boxed{\text{36}^\circ}$.
The larger angle is $\boxed{\text{144}^\circ}$.