Answer :

GinnyAnswer
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°.

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