Certainly! Let's solve this problem step-by-step.
1. Given: One of the exterior angles of an isosceles triangle is 30°.
2. Step 1: Find the corresponding interior angle.
The exterior angle of a triangle is the supplement of the interior angle at that vertex. Therefore, if the exterior angle is 30°, the corresponding interior angle is:
[tex]\[
180° - 30° = 150°
\][/tex]
3. Step 2: Use properties of an isosceles triangle.
In an isosceles triangle, two of the interior angles are equal. Let's identify these two angles as the base angles.
4. Step 3: Set up an equation involving the base angles.
In a triangle, the sum of the interior angles is always 180°. Let the two equal base angles be [tex]\( x \)[/tex]. Therefore, we have the equation:
[tex]\[
2x + 150° = 180°
\][/tex]
5. Step 4: Solve for [tex]\( x \)[/tex].
Simplify and solve the equation:
[tex]\[
2x + 150° = 180°
\][/tex]
Subtract 150° from both sides:
[tex]\[
2x = 30°
\][/tex]
Divide both sides by 2:
[tex]\[
x = 15°
\][/tex]
So, the other two angles of the isosceles triangle are each 15°.
