单选题In quadrilateral ABCD, ∠A +∠C is 2 times ∠B +∠D. If ∠A = 40, then ∠B = ______.A60B80C120D240EIt cannot be determined from the information given.
单选题
In quadrilateral ABCD, ∠A +∠C is 2 times ∠B +∠D. If ∠A = 40, then ∠B = ______.
A
60
B
80
C
120
D
240
E
It cannot be determined from the information given.
参考解析
解析：
You are given that, in quadrilateral ABCD, ∠A+∠C is 2 times ∠XB+∠D, and ∠A = 40, so
40+∠C = 2(∠B+∠D). Since the sum of the degree measures of the four angles of a quadrilateral is 360, 40+∠C+(∠B+∠D) = 360. Substituting 2(∠B+∠D) for 40+∠C gives. 2(∠B+∠D)+(∠B+∠D) = 360. Since the last equation contains two unknowns, the measures of angles B and D, it is not possible to find the measure of ∠B (or ∠D).
You are given that, in quadrilateral ABCD, ∠A+∠C is 2 times ∠XB+∠D, and ∠A = 40, so
40+∠C = 2(∠B+∠D). Since the sum of the degree measures of the four angles of a quadrilateral is 360, 40+∠C+(∠B+∠D) = 360. Substituting 2(∠B+∠D) for 40+∠C gives. 2(∠B+∠D)+(∠B+∠D) = 360. Since the last equation contains two unknowns, the measures of angles B and D, it is not possible to find the measure of ∠B (or ∠D).
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