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

a sprinkler swings back and forth between A and B in such a way that lt1 lt2lt1 and lt3are complementary and lt2and lt4 are complementary if mlt1475find mlt2mlt class=

Respuesta :

Given data:

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

The expression for the angle 2 is,

[tex]\begin{gathered} m\angle2=m\angle1 \\ m\angle2=47.5^{\circ} \end{gathered}[/tex]

The expression for the complementary angle is,

[tex]\begin{gathered} m\angle1+m\angle3=90^{\circ} \\ 47.5^{\circ}+m\angle3=90^{\circ} \\ m\angle3=42.5^{\circ} \end{gathered}[/tex]

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

[tex]\begin{gathered} m\angle2+m\angle4=90^{\circ} \\ 47.5^{\circ}+m\angle4=90^{\circ} \\ m\angle4=42.5^{\circ} \end{gathered}[/tex]

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