In the figure shown, what is the measure of angle x?

triangle abc has measure of angle bac equal to 30 degrees and the measure of angle abc is equal to 75 degrees. the side bc of the triangle is extended till d. the angle acd is labeled as x.

150 degrees
110 degrees
105 degrees
100 degrees

Your x angle here is supplementary to the missing angle of the triangle, the "missing angle" of the triangle is the same as <B - which is 75 degrees. So; to solve x, 180-75=x

x=105

Step-by-step explanation:

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west