Final answer:
To find the measure of angle ∠2 in an isosceles triangle ABC, we can set up an equation using the given angles ∠1 and ∠3. By solving the equation, we find that ∠2 is equal to 74°.
Step-by-step explanation:
Given that AB and AC are the legs of an isosceles triangle ABC and ∠1 = 5x, ∠3 = 2x + 12, we need to find ∠2.
Since AB and AC are the legs of an isosceles triangle, ∠1 and ∠3 are congruent. Therefore, 5x = 2x + 12. Solving this equation, we get x = 4. Substituting this value into ∠1, we find that ∠1 = 20°.
Since ∠2 and ∠3 are supplementary angles in a triangle, we have ∠2 + ∠3 = 180°. Substituting the values ∠1 = 20° and ∠3 = 2x + 12, we can solve for ∠2. 20° + (2x + 12) = 180°, which gives us 2x = 148° and x = 74°. Therefore, ∠2 = 74°.