Question

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

Answer 1

Explanation

From the statement, we know that:

• ∠ABC ≅ ∠EFG,

• ∠ABC = (4x + 3)°,

• ∠EFG = (2x + 11)°.

(1) Using the data from above, we have:

$\begin{gathered} ∠ABC\cong∠EFG, \\ (4x+3)\degree=(2x+11)\degree, \\ 4x+3=2x+11. \end{gathered}$

(2) Solving for x the last equation:

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

(3) Replacing the value x = 4 in the equations of the first angle, we get:

$∠ABC=(4\cdot4+3)°=(16+3)\degree=19\degree.$Answer

m∠ABC = m∠EFG = 19°