Question

2 fill in the blank 1 point
in the figure above,

1. x =
2. the measure of $angle bcd$ =
3. the measure of $angle bac$ =

Explanation:

Step1: Use exterior angle theorem

The exterior angle of a triangle equals the sum of the two non-adjacent interior angles, so:
$$5x + 14 = (3x - 10) + 46$$

Step2: Simplify and solve for $x$

Simplify the right-hand side, then isolate $x$:
$$5x + 14 = 3x + 36$$
$$5x - 3x = 36 - 14$$
$$2x = 22$$
$$x = \frac{22}{2} = 11$$

Step3: Calculate $\angle BCD$

Substitute $x=11$ into $5x+14$:
$$\angle BCD = 5(11) + 14 = 55 + 14 = 69$$

Step4: Calculate $\angle BAC$

Substitute $x=11$ into $3x-10$:
$$\angle BAC = 3(11) - 10 = 33 - 10 = 23$$

Answer:

1. $x = 11$
2. The measure of $\angle BCD = 69^\circ$
3. The measure of $\angle BAC = 23^\circ$