One angle = 60.
In the figure above, point D divides side BC of triangle ABC into segments BD and DC of lengths 1 and 2 units respectively. Given that Angle ADC = 60 and Angle ABD = 45, what is the measure of angle x? (Note: Figure is not drawn to scale.)
(A) 55
(B) 60
(C) 70
(D) 75
(E) 90
Another angle = 45.
Look for 30-60-90 and 45-45-90 triangles.
Click on the figures below to enlarge them.
Step 1:
Draw 30-60-90 ∆CDE.
Result:
DE=BD=1.
Step 2:
Since DE=BD, draw ISOSCELES ∆BDE.
Add to the figure the implied angle measurements, as shown above.
Step 3:
Notice that ∆BCE and ∆ABE are also ISOSCELES.
Step 4:
Since BC=CE=AE, ∆ACE also is ISOSCELES.
Add to the figure the implied angle measurements, as shown above.
Result:
∠ACD = 45+30 = 75.
The correct answer is D.
