Question

find the value of x in the isosceles triangle.

Explanation:

Step1: Recall isosceles triangle property

In an isosceles triangle, the angles opposite equal sides are equal. So, $\angle B = \angle C$? Wait, no, the sides AB and AC are equal (marked with ticks), so the base angles $\angle B$ and $\angle C$? Wait, no, AB and AC are the equal sides, so the base is BC, so the base angles are $\angle B$ and $\angle C$? Wait, no, in triangle ABC, AB = AC (ticks), so the angles opposite them are $\angle C$ and $\angle B$ respectively. Wait, angle opposite AB is $\angle C$, angle opposite AC is $\angle B$. So if AB = AC, then $\angle B = \angle C$? Wait, no, the diagram shows $\angle B$ is $4x$ and $\angle C$ is $80^\circ$. Wait, maybe I got it wrong. Wait, the equal sides are AB and AC, so the base is BC, so the base angles are $\angle B$ and $\angle C$? Wait, no, in an isosceles triangle with AB = AC, the base is BC, so the base angles are $\angle B$ and $\angle C$, so they should be equal. Wait, but in the diagram, $\angle B$ is $4x$ and $\angle C$ is $80^\circ$. Wait, maybe that's a mistake? Wait, no, maybe I misread. Wait, the problem says "isosceles triangle", and the sides AB and AC are marked equal (ticks), so $\angle B = \angle C$? Wait, but $\angle B$ is $4x$ and $\angle C$ is $80^\circ$, so $4x = 80^\circ$? Wait, that would make $x = 20$. Wait, let's check.

Step2: Set up the equation

Since AB = AC, $\angle B = \angle C$. So $4x = 80^\circ$.

Step3: Solve for x

Divide both sides by 4: $x = \frac{80^\circ}{4} = 20^\circ$. Wait, but angles are in degrees, but the variable x is just a value, so $x = 20$.

Answer:

20