Question

a sprinkler swings back and forth between A and B in such a way that <1 <2,<1 and <3are complementary, and <2and <4 are complementary if m<1=4.75°,find m<2,m<3 and m<4 the measure of <2 is the measure of <3is the measure of <4 is

Answer 1

Given data:

The measure of the first angle is m∠1=47.5°.

The expression for the angle 2 is,

`\begin{gathered} m\angle2=m\angle1 \\ m\angle2=47.5^(\circ) \end{gathered}`

The expression for the complementary angle is,

`\begin{gathered} m\angle1+m\angle3=90^(\circ) \\ 47.5^(\circ)+m\angle3=90^(\circ) \\ m\angle3=42.5^(\circ) \end{gathered}`

The expression for the second pair of the complementary angle is,

`\begin{gathered} m\angle2+m\angle4=90^(\circ) \\ 47.5^(\circ)+m\angle4=90^(\circ) \\ m\angle4=42.5^(\circ) \end{gathered}`

Thus, the value of m∠2=47.5°, the value of m∠3=42.5°, and the value of m∠4=42.5°.