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11. In \( \triangle W X Y \), if \( m \angle W \) is five less than twice \( m \angle Y \) and \( m \angle X \) is 21 more than \( m \angle Y \), find the measure of each angle.

Ask by Phillips Colon. in the United States
Jan 24,2025

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The measures of the angles are: - \( m \angle W = 77^\circ \) - \( m \angle X = 62^\circ \) - \( m \angle Y = 41^\circ \)

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Mind Expander

Let's denote the measure of angle \( Y \) as \( y \). According to the problem, we have: - \( m \angle W = 2y - 5 \) - \( m \angle X = y + 21 \) Using the fact that the sum of the angles in a triangle is \( 180^\circ \): \[ m \angle W + m \angle X + m \angle Y = 180 \] Substituting for \( m \angle W \) and \( m \angle X \): \[ (2y - 5) + (y + 21) + y = 180 \] Now, combine the terms: \[ 2y - 5 + y + 21 + y = 180 \] This simplifies to: \[ 4y + 16 = 180 \] Next, isolate \( y \) by subtracting 16 from both sides: \[ 4y = 164 \] Then divide by 4: \[ y = 41 \] Now that we have \( m \angle Y \) (which is \( 41^\circ \)), we can find the other angles: 1. For \( m \angle W \): \[ m \angle W = 2(41) - 5 = 82 - 5 = 77^\circ \] 2. For \( m \angle X \): \[ m \angle X = 41 + 21 = 62^\circ \] Thus, the measures of the angles in triangle \( WXY \) are: - \( m \angle W = 77^\circ \) - \( m \angle X = 62^\circ \) - \( m \angle Y = 41^\circ \)

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