Question

Find m<YDC
please help!​

Answer 1

∠YDC measures 140°.

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:

`\displaystyle m \angle YDC = m\angle DCB + m\angle CBD`

Substitute:

`\displaystyle (15x + 5) = (80) + (6x+6)`

Solve for x. Combine like terms:

`15x + 5 = 6x + 86`

Simplify:

`9x = 81`

And divide. Hence, the value of x is:

`x = 9`

∠YDC is given by:

`\displaystyle m\angle YDC = 15x + 5`

Since we now know the value of x, substitute and evaluate:

`\displaystyle \begin{aligned} m\angle YDC &= 15x + 5 \\ &= 15(9) + 5 \\ &= 135 + 5 \\ &= 140^\circ\end{aligned}`

In conclusion, ∠YDC measures 140°.