To find the measures of the two unknown angles in the quadrilateral, we first need to use the fact that the sum of the angles in any quadrilateral is \(360^\circ\).
Given:
- The first two angles measure \(300^\circ\) and \(28^\circ\).
- Let the two unknown angles be \(x\) and \(y\), with the given ratio \(x:y = 7:9\).
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First, calculate the sum of the known angles: \[ 300^\circ + 28^\circ = 328^\circ \]
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Calculate the sum of the unknown angles: \[ x + y = 360^\circ - 328^\circ = 32^\circ \]
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Since \(x\) and \(y\) are in the ratio \(7:9\), we can express them in terms of a variable \(k\): \[ x = 7k \quad \text{and} \quad y = 9k \]
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Substitute these expressions into the equation for the sum of the angles: \[ 7k + 9k = 32^\circ \] \[ 16k = 32^\circ \] \[ k = 2^\circ \]
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Now, substitute \(k = 2^\circ\) back into the expressions for \(x\) and \(y\): \[ x = 7k = 7 \times 2^\circ = 14^\circ \] \[ y = 9k = 9 \times 2^\circ = 18^\circ \]
Thus, the measures of the two unknown angles are: \[ \text{First angle: } 14^\circ \] \[ \text{Second angle: } 18^\circ \]
Final answer: 14° and 18°
2 answers