Question

∠1 and ∠2 are complementary angles. if ( mangle 1 = (x - 1)^circ ) and ( mangle 2 = (4x - 4)^circ ), then find the measure of ( angle 1 ).

Explanation:

Step1: 互补角和为90°

因为\(\angle1\)和\(\angle2\)是互补角，所以\(m\angle1 + m\angle2 = 90^\circ\)，即\((x - 1) + (4x - 4) = 90\)。

Step2: 解方程求x

展开式子得\(x - 1 + 4x - 4 = 90\)，合并同类项得\(5x - 5 = 90\)，两边加5得\(5x = 95\)，两边除以5得\(x = 19\)。

Step3: 求\(\angle1\)的度数

将\(x = 19\)代入\(m\angle1 = (x - 1)^\circ\)，得\(m\angle1 = (19 - 1)^\circ = 18^\circ\)。

Answer:

\(18^\circ\)