The figure shows adjacent angles BAC and CAD.

Question

Adjacent angles BAC and CAD sharing common ray AC

Given:
m∠BAD = 129°
m∠BAC = (2x −1)°
m∠CAD = (3x + 5)°

Part A: Using the angle addition postulate, write and solve an equation for x. Show all your work. (6 points)

Part B: Find the m∠BAC. Show all your work. (4 points)

(Please complete everything in regular font. No titles, no headings, etcetera.)

Answer 1

We know that angles BAC and CAD are adjacent angles that share the common ray AC. According to the angle addition postulate, the sum of these two angles equals the measure of the larger angle, BAD. Therefore, we can write the equation:

m∠BAC + m∠CAD = m∠BAD

Substituting in the measures given:

(2x - 1) + (3x + 5) = 129°

Now, combine like terms:

2x - 1 + 3x + 5 = 129° 5x + 4 = 129°

Next, we isolate x by subtracting 4 from both sides:

5x = 129° - 4 5x = 125°

Now, divide both sides by 5:

x = 125° / 5 x = 25°

Part B: Now that we have x, we can find m∠BAC.

Substituting x back into the equation for m∠BAC:

m∠BAC = (2x - 1)° m∠BAC = (2(25) - 1)° m∠BAC = (50 - 1)° m∠BAC = 49°

Therefore, m∠BAC = 49°.