Question

solve for x. then find the measure of angle ydc.
x =
m∠ydc =

Explanation:

Step1: Use the exterior - angle theorem

The exterior - angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent interior angles.
So, \(15x + 5=(6x + 6)+80\).

Step2: Solve the equation for \(x\)

$$
LATEXBLOCK0
$$

Step3: Find the measure of \(\angle YDC\)

Substitute \(x = 9\) into the expression for \(\angle YDC\) (\(15x + 5\)).
\(m\angle YDC=15x+5\), when \(x = 9\), \(m\angle YDC=15\times9 + 5=135+5 = 140^{\circ}\)

Answer:

\(x = 9\), \(m\angle YDC=140^{\circ}\)