Answer:
∠YDC measures 140°.
Step-by-step explanation:
We can consider using the Exterior Angle Theorem. According to the theorem, the exterior angle of a triangle is equal to the two opposite interior angles.
In other words:
[tex]\displaystyle m \angle YDC = m\angle DCB + m\angle CBD[/tex]
Substitute:
[tex]\displaystyle (15x + 5) = (80) + (6x+6)[/tex]
Solve for x. Combine like terms:
[tex]15x + 5 = 6x + 86[/tex]
Simplify:
[tex]9x = 81[/tex]
And divide. Hence, the value of x is:
[tex]x = 9[/tex]
∠YDC is given by:
[tex]\displaystyle m\angle YDC = 15x + 5[/tex]
Since we now know the value of x, substitute and evaluate:
[tex]\displaystyle \begin{aligned} m\angle YDC &= 15x + 5 \\ &= 15(9) + 5 \\ &= 135 + 5 \\ &= 140^\circ\end{aligned}[/tex]
In conclusion, ∠YDC measures 140°.
