11. In $$ riangle W X Y $$, 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.

Question

11. In $$ 	riangle W X Y $$, 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.

UpStudy AI · Accepted Answer

Let’s determine the measures of the angles in triangle $$ \triangle WXY $$ using the given relationships.

1. **Define the Variables:**
   - Let $$ m \angle Y = y $$ degrees.
   - Then, according to the problem:
     - $$ m \angle W = 2y - 5 $$ degrees.
     - $$ m \angle X = y + 21 $$ degrees.

2. **Use the Triangle Angle Sum Property:**
   The sum of the angles in any triangle is $$ 180^\circ $$. Therefore:
   $$
   m \angle W + m \angle X + m \angle Y = 180
   $$
   Substitute the expressions for each angle:
   $$
   (2y - 5) + (y + 21) + y = 180
   $$
   
3. **Solve for $$ y $$:**
   Combine like terms:
   $$
   2y - 5 + y + 21 + y = 180
   $$
   $$
   4y + 16 = 180
   $$
   Subtract 16 from both sides:
   $$
   4y = 164
   $$
   Divide by 4:
   $$
   y = 41
   $$
   
4. **Find Each Angle:**
   - $$ m \angle Y = 41^\circ $$
   - $$ m \angle W = 2(41) - 5 = 82 - 5 = 77^\circ $$
   - $$ m \angle X = 41 + 21 = 62^\circ $$

5. **Verification:**
   $$
   77^\circ + 62^\circ + 41^\circ = 180^\circ
   $$
   The angles sum up correctly.

**Final Answer:**
- $$ m \angle W = 77^\circ $$
- $$ m \angle X = 62^\circ $$
- $$ m \angle Y = 41^\circ $$
The measures of the angles are: - $$ m \angle W = 77^\circ $$ - $$ m \angle X = 62^\circ $$ - $$ m \angle Y = 41^\circ $$

In , if is five less than twice and is 21 more than , find the
measure of each angle.

Solución de inteligencia artificial de Upstudy

Responder

Solución

Mind Expander

preguntas relacionadas

Latest Geometry Questions

In , if is five less than twice and is 21 more than , find the measure of each angle.