Question

1. in $\triangle wxy$, 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.

$m\angle w = \underline{\quad\quad}$
$m\angle x = \underline{\quad\quad}$
$m\angle y = \underline{\quad\quad}$

Explanation:

Step1: Define variables for angles

Let \( m\angle Y = x \). Then \( m\angle W = 2x - 5 \) (since \( m\angle W \) is five less than twice \( m\angle Y \)) and \( m\angle X = x + 21 \) (since \( m\angle X \) is 21 more than \( m\angle Y \)).

Step2: Use triangle angle sum theorem

In a triangle, the sum of angles is \( 180^\circ \). So, \( m\angle W + m\angle X + m\angle Y = 180 \). Substitute the expressions: \( (2x - 5) + (x + 21) + x = 180 \).

Step3: Simplify and solve for x

Combine like terms: \( 2x - 5 + x + 21 + x = 180 \) → \( 4x + 16 = 180 \). Subtract 16: \( 4x = 164 \). Divide by 4: \( x = 41 \).

Step4: Find each angle measure

• \( m\angle Y = x = 41^\circ \)
• \( m\angle W = 2x - 5 = 2(41) - 5 = 77^\circ \)
• \( m\angle X = x + 21 = 41 + 21 = 62^\circ \)

Answer:

\( m\angle W = 77^\circ \), \( m\angle X = 62^\circ \), \( m\angle Y = 41^\circ \)