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 \( 44^{\circ} \). The measure of the second angle is

To solve this problem, let's denote the measure of the second angle as \( x \). According to the problem, the first angle is twice the second angle, so it can be expressed as \( 2x \), and the third angle can be expressed as \( x + 92 \). We know that the sum of the angles in a triangle equals \( 180^{\circ} \). Therefore, we can set up the equation: \[ 2x + x + (x + 92) = 180 \] This simplifies to: \[ 4x + 92 = 180 \] Subtract \( 92 \) from both sides: \[ 4x = 180 - 92 \] \[ 4x = 88 \] Now, divide both sides by \( 4 \): \[ x = 22 \] So, the measure of the second angle is \( 22^{\circ} \). Now, using the measure of the second angle we can find the other angles: - The first angle: \( 2x = 2(22) = 44^{\circ} \) - The third angle: \( x + 92 = 22 + 92 = 114^{\circ} \) In conclusion, the measures of the angles in the triangle are: - First angle: \( 44^{\circ} \) - Second angle: \( 22^{\circ} \) - Third angle: \( 114^{\circ} \)