Question

Find m<YDC please help!​

Answer 1

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:

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

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°.