Question

question
in δcde, m∠c = (4x - 3)°, m∠d = (5x - 6)°, and m∠e = (x - 1)°. what is the value of x?
answer attempt 1 out of 2

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \(m\angle C + m\angle D + m\angle E = 180^\circ\).

Step2: Substitute angle expressions

Substitute \(m\angle C=(4x - 3)^\circ\), \(m\angle D=(5x - 6)^\circ\), \(m\angle E=(x - 1)^\circ\) into the equation:
\((4x - 3)+(5x - 6)+(x - 1)=180\).

Step3: Combine like terms

Combine \(x\)-terms and constants:
\(4x + 5x + x-3 - 6 - 1 = 180\)
\(10x-10 = 180\).

Step4: Solve for \(x\)

Add 10 to both sides: \(10x = 190\).
Divide by 10: \(x = 19\).

Answer:

\(19\)