Question

In the ΔXYZ, ∠X and ∠Z are congruent. If m∠X=(3x+14)°and m∠Z=53°, find the value of x.

Answer 1

Step-by-step explanation

From the statement, we know that:

• ∠X and ∠Z are congruent ⇒ m∠X = m∠Z,

• m∠X= (3x+14)°,

• m∠Z = 53°.

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

`\begin{gathered} m∠X=m∠Z, \\ (3x+14)\degree=53\degree, \\ 3x+14=53. \end{gathered}`

(2) Solving the last equation for x, we get:

`\begin{gathered} 3x=53-14, \\ 3x=39, \\ x=(39)/(3)=13. \end{gathered}`Answer

x = 13