Suppose ∠ABC≅∠EFG∠ABC≅∠EFG. If m∠ABC=(4x+3)°m∠ABC=(4x+3)° and m∠EFG=(2x+11)°m∠EFG=(2x+11)°, find the actual measurements of the two angles

Respuesta :

Recall that congruent angles have the same measure.

Since ∠ABC≅∠EFG, then:

[tex]m\angle ABC=m\angle EFG.[/tex]

Therefore:

[tex](4x+3)^{\circ}=(2x+11)^{\circ}.[/tex]

Then:

[tex]4x+3=2x+11.[/tex]

Adding -3-2x to the above equation we get:

[tex]\begin{gathered} 4x+3-3-2x=2x+11-3-2x, \\ 2x=8. \end{gathered}[/tex]

Dividing the above equation by 2 we get:

[tex]\begin{gathered} \frac{2x}{2}=\frac{8}{2}, \\ x=4. \end{gathered}[/tex]

Therefore:

[tex]\begin{gathered} m\angle ABC=(4*4+3)^{\circ}=(16+3)^{\circ}=19^{\circ}, \\ m\angle EFG=(2*4+11)^{\circ}=(8+11)^{\circ}=19^{\circ}. \end{gathered}[/tex]

Answer:

[tex]\begin{gathered} m\angle ABC=19^{\circ}, \\ m\angle EFG=19^{\circ}. \end{gathered}[/tex]