Question

∠1 and ∠2 are complementary angles. if ( mangle 1 = (8x - 11)^circ ) and ( mangle 2 = (6x - 25)^circ ), then find the measure of ( angle 1 ).

Explanation:

Step1: 互补角和为90°

因为∠1和∠2互补，所以\(m\angle1 + m\angle2 = 90^\circ\)，即\((8x - 11) + (6x - 25) = 90\)。

Step2: 解方程求x

合并同类项得\(14x - 36 = 90\)，移项得\(14x = 90 + 36 = 126\)，解得\(x = \frac{126}{14} = 9\)。

Step3: 求∠1的度数

将\(x = 9\)代入\(m\angle1 = 8x - 11\)，得\(m\angle1 = 8\times9 - 11 = 72 - 11 = 61\)。

Answer:

\(61^\circ\)