Question

1. since $angle c$ and $angle d$ are choose your answer..., the correct equation is choose your answer...2. the value of x = type your answer...3. the measure of angle c = type your answer...4. the measure of the exterior angle, $angle abd$ = type your answer...

Explanation:

Step1: Identify angle relationship

$\angle C$ and $\angle D$ are the remote interior angles to exterior $\angle ABD$, so the exterior angle equals the sum of the two remote interior angles.
Equation: $20x = (7x + 5) + 60$

Step2: Solve for $x$

Simplify and isolate $x$:
$20x = 7x + 65$
$20x - 7x = 65$
$13x = 65$
$x = \frac{65}{13} = 5$

Step3: Calculate $\angle C$

Substitute $x=5$ into $7x+5$:
$\angle C = 7(5) + 5 = 35 + 5 = 40$

Step4: Calculate $\angle ABD$

Substitute $x=5$ into $20x$:
$\angle ABD = 20(5) = 100$

Answer:

1. Since $\angle C$ and $\angle D$ are remote interior angles, the correct equation is $20x=(7x+5)+60$
2. $x = 5$
3. The measure of angle $C = 40^\circ$
4. The measure of the exterior angle $\angle ABD = 100^\circ$