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Ray VD bisects angle CVE. m angle CVD=20x+4, and m angle EVD=14x+22. Solve for x, and give the angle measures for all three angles.

Ray VD Bisects Angle CVE M Angle CVD20x4 And M Angle EVD14x22 Solve For X And Give The Angle Measures For All Three Angles class=

Sagot :

We know that

• Ray VD bisects angle CVE.

,

• Angle CVD = 20x+4

,

• Angle EVD = 14x+22

If VD bisects CVE, then angle CVD and EVD are equal, that means

[tex]\begin{gathered} m\angle CVD=m\angle EVD \\ 20x+4=14x+22 \end{gathered}[/tex]

Now, we solve for x. First, we subtract 4 on each side

[tex]\begin{gathered} 20x+4-4=14x+22-4 \\ 20x=14x+18 \end{gathered}[/tex]

Then, we subtract 14x on each side

[tex]\begin{gathered} 20x-14x=14x+18-14x \\ 6x=18 \end{gathered}[/tex]

At last, we divide the equation by 6

[tex]\begin{gathered} \frac{6x}{6}=\frac{18}{6} \\ x=3 \end{gathered}[/tex]

With this value, we find each angle.

[tex]m\angle CVD=20x+4=20(3)+4=60+4=64[/tex][tex]m\angle EVD=14x+22=14(3)+22=42+22=64[/tex]

Therefore, each angle measures 64°, and the whole angle CVE measures 128°.

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