Question

5. 8.G.1.5 Right triangle ABC and right triangle ACD overlap as shown below. Angle DAC measures 20° and angle BCA measures 30°. B D to 20- A 30° C not drawn to scale What are the values of and y?

Answer 1

In any triangle, the sum of the internal angle is always up to 180º.

Then, for triangle ABC:

`90º+30º+(x+20º)=180º`

Use it to solve x:

`\begin{gathered} 90º+30º+x+20º=180º \\ x=180º-90º-30º-20º \\ x=40º \end{gathered}`

In the triangle ACD:

`90º+20º+(y+30º)=180º`

Use it to solve y:

`\begin{gathered} 90º+20º+y+30º=180º \\ y=180º-90º-20º-30º \\ y=40º \end{gathered}`Then, the value for x is 40º and the value for y is also 40º