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In the figure above, if BC = CD and angle ADC = 90 degrees, then what is the value of x?
A. 45
B. 50
C. 70
D. 75
E. 100
Attachment:
2016-01-04_0031.png [ 6.39 KiB | Viewed 6065 times ]
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[quote="Bunuel"]
In the figure above, if BC = CD and angle ADC = 90 degrees, then what is the value of x?
angle BDC also = 70
90-70=20
angle ABD=180-70=110
180-110-20
=50
B. 50
In the figure above, if BC = CD and angle ADC = 90 degrees, then what is the value of x?
angle BDC also = 70
90-70=20
angle ABD=180-70=110
180-110-20
=50
B. 50
Slightly longer method:
1. CBD = 70
2. Due to the isosceles triangle angle rules, BDC = 70
3. BCD = 180 - 70 - 70
4. BCD = 40
5. BAD (angle x) = 180 - 90 (due to right triangle) - 40
6. BAD (angle x) = 50
The answer is B, x = 50.
1. CBD = 70
2. Due to the isosceles triangle angle rules, BDC = 70
3. BCD = 180 - 70 - 70
4. BCD = 40
5. BAD (angle x) = 180 - 90 (due to right triangle) - 40
6. BAD (angle x) = 50
The answer is B, x = 50.
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Bunuel
BC=CD means angle CBD = CDB =70 and angle BCD=40. BCD+CDA+CAD=180 -> 40+90+x=180, hence x=50
Answer B
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Expert reply
Posts: 22,737
Bunuel
We can use triangle ABD to determine the value of x (since the angle with x degrees is angle A of triangle ABD). Let’s first determine the measures of the other two angles, angle ABD and angle BDA.
Using the given diagram, we see that angle ABD = 180 - 70 = 110 degrees.
Since BC = CD, angle CBD = angle CDB. Since angle CBD = 70 degrees, angle CDB = 70 degrees. Furthermore, angle BDA = 90 - 70 = 20 degrees.
Since we know the measures of the other two angles, x = angle A = 180 - 110 - 20 = 50 degrees.
Answer: B
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