Question

question
triangle ijk is formed by connecting the mid - points of the side of triangle fgh. the measures of the interior angles of triangle fgh are shown. find the measure of ∠fki. figures not necessarily drawn to scale.
answer attempt 1 out of 2
m∠fki =
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Explanation:

Step1: Recall mid - point triangle property

When a triangle is formed by connecting the mid - points of the sides of another triangle (mid - point triangle), the mid - point triangle is similar to the original triangle and corresponding angles are equal.

Step2: Identify corresponding angles

$\angle FKI$ and $\angle FGH$ are corresponding angles. Since $\triangle IJK$ is formed by connecting the mid - points of the sides of $\triangle FGH$, $\angle FKI=\angle FGH$.

Step3: Determine the angle measure

Given that $m\angle FGH = 106^{\circ}$, so $m\angle FKI=106^{\circ}$.

Answer:

$106^{\circ}$