Questions: Find m∠KLJ.

Transcript text: Find $\mathrm{m} \angle K L J$.

Solution

Step 1: Identify the Given Information

The problem provides a triangle $ \triangle KLJ $ with $ \angle KJL = 52^\circ $. The triangle is isosceles with $ KL = LJ $.

Step 2: Use the Properties of an Isosceles Triangle

In an isosceles triangle, the base angles are equal. Therefore, $ \angle KJL = \angle KJL = 52^\circ $.

Step 3: Apply the Triangle Angle Sum Property

The sum of the angles in any triangle is $ 180^\circ $. Let $ \angle KLJ = x $. Then: \[ x + 52^\circ + 52^\circ = 180^\circ \]

Step 4: Solve for $ x $

\[ x + 104^\circ = 180^\circ \] \[ x = 180^\circ - 104^\circ \] \[ x = 76^\circ \]

The measure of $ \angle KLJ $ is $ 76^\circ $.

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