In triangle ABC above, if ∠BAD and ∠ADB ha

问题单项选择题

In triangle ABC above, if ∠BAD and ∠ADB have measures of 4n, ∠ACB has a measure of n, and ∠DBC has a measure of 45°, what is the measure of ∠ABC ？（） (Figure not necessarily drawn to scale.)

A. 45°

B. 60°

C. 90°

D. 105°

E. 120°

答案

参考答案：D

解析：

The principle to remember here is that an exterior angle of a triangle--such as ∠ADB--is equal to the sum of the remote interior angles of the triangle, in this case ∠DBC and ∠DCB (=∠ACB) of triangle BDC. Thus, ∠DCB+∠DBC=4n, or ∠DBC=3n=45°, and therefore n=15° and 4n=60°. The three angles of a triangle must equal 180°, so ∠ABC=180°-60°-15°=105°.