Question

1. if ( \triangle mtwcong\triangle bgk ), find the values of ( x ) and ( y ).

Explanation:

Step1: Use the property of congruent triangles (corresponding angles are equal)

Since \(\triangle MTV\cong\triangle BGK\), then \(\angle VMT=\angle KBG\) and \(\angle TVM = \angle GBK\).
We know that \(\angle VMT = 41^{\circ}\), \(\angle TVM=(4x - 3)^{\circ}\), \(\angle KBG = 45^{\circ}\), \(\angle GBK=(11y + 6)^{\circ}\)

For \(x\):
Because \(\angle TVM=\angle GBK\) (corresponding angles of congruent triangles), we set up the equation \(4x-3 = 45\)

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Step2: For \(y\)

Because \(\angle VMT=\angle KBG\) (corresponding angles of congruent triangles), we set up the equation \(11y+6=41\)

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Answer:

\(x = 12\), \(y=\frac{35}{11}\)