Question

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1. if $\triangle abc \sim \triangle efg$, $m\angle c = 4x + 30$, and $m\angle g = 5x + 10$. determine the value of $x$.

Explanation:

Step1: Recall Similar Triangles Property

In similar triangles, corresponding angles are equal. So, \( m\angle C = m\angle G \).

Step2: Set Up the Equation

Given \( m\angle C = 4x + 30 \) and \( m\angle G = 5x + 10 \), we set them equal:
\( 4x + 30 = 5x + 10 \)

Step3: Solve for \( x \)

Subtract \( 4x \) from both sides:
\( 30 = x + 10 \)
Subtract 10 from both sides:
\( x = 20 \)

Answer:

\( x = 20 \)