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Leo34005
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Two angles∠3 and ∠5 are each supplementary to ∠4. If m∠5 is 78°, what is m∠3?
Two angles∠3 and ∠5 are each supplementary to ∠4. If m∠5 is 78°, what is m∠3?
A) 102°
B) 2°
C) 78°
D) 90°
E) 180°
If two angles are supplements, their sum is 180 degrees.
Algebraic solution:
measure ∠5 = 78 degrees
measure ∠4 = x (we do not know the measure of this angle yet, so it's x)
So: 78 + x = 180 degrees
^^[because these angles are supplements, we know they have to equal 180 degrees]
If you solve that you find out that x, or measure ∠4, is 102 degrees. Check that by doing 78 + 102 = 180.
Since ∠3 is also supplementary to angle 4, ∠3 = ∠5
Which means ∠3 is 78 degrees.
We have discovered:
Measure ∠4 = 102 degrees
Measure ∠5 = 78 degrees
Measure ∠3 = 78 degrees
Final answer is C) 78°
Two angles∠3 and ∠5 are each supplementary to ∠4. If m∠5 is 78°, what is m∠3?
A) 102°
B) 2°
C) 78°
D) 90°
E) 180°
If two angles are supplements, their sum is 180 degrees.
Algebraic solution:
measure ∠5 = 78 degrees
measure ∠4 = x (we do not know the measure of this angle yet, so it's x)
So: 78 + x = 180 degrees
^^[because these angles are supplements, we know they have to equal 180 degrees]
If you solve that you find out that x, or measure ∠4, is 102 degrees. Check that by doing 78 + 102 = 180.
Since ∠3 is also supplementary to angle 4, ∠3 = ∠5
Which means ∠3 is 78 degrees.
We have discovered:
Measure ∠4 = 102 degrees
Measure ∠5 = 78 degrees
Measure ∠3 = 78 degrees
Final answer is C) 78°
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