Question

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

Answer 1

Recall that congruent angles have the same measure.

Since ∠ABC≅∠EFG, then:

`m\angle ABC=m\angle EFG.`

Therefore:

`(4x+3)^(\circ)=(2x+11)^(\circ).`

Then:

`4x+3=2x+11.`

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

`\begin{gathered} 4x+3-3-2x=2x+11-3-2x, \\ 2x=8. \end{gathered}`

Dividing the above equation by 2 we get:

`\begin{gathered} (2x)/(2)=(8)/(2), \\ x=4. \end{gathered}`

Therefore:

`\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}`

Answer:

`\begin{gathered} m\angle ABC=19^(\circ), \\ m\angle EFG=19^(\circ). \end{gathered}`