In a triangle, the measure of the first angle is twice the measure of the second angle. The measure of the third angle is \( 92^{\circ} \) more than the measure of the second angle. Use the fact that the sum of the measures of the three angles of a triangle is \( 180^{\circ} \) to find the measure of each angle. The measure of the first angle is \( \square^{\circ} \).

Let the measure of the second angle be \( x \). Then, the first angle can be expressed as \( 2x \) and the third angle as \( x + 92 \). According to the triangle angle sum property, we can write the equation: \[ 2x + x + (x + 92) = 180 \] Simplifying this, we get: \[ 4x + 92 = 180 \] Now, subtracting 92 from both sides gives: \[ 4x = 180 - 92 \] \[ 4x = 88 \] Dividing by 4, we find: \[ x = 22 \] Now we can find the measures of the angles: - Second angle: \( x = 22^{\circ} \) - First angle: \( 2x = 2 \times 22 = 44^{\circ} \) - Third angle: \( x + 92 = 22 + 92 = 114^{\circ} \) Therefore, the measure of the first angle is \( 44^{\circ} \). Isn't it fascinating how such relationships unfold in triangles? Just a few variables, and suddenly you can unlock angles like a geometric detective!