| The measures of two angles of a triangle is in the ratio 4: 5. If the sum of these two measures is equal to the measure of the third angle. Find the smallest angle. |
A) \[90{}^\circ \]
B) \[50{}^\circ \]
C) \[10{}^\circ \]
D) \[40{}^\circ \]
Correct Answer: D
Solution :
| Measures of all the three angles of the triangle |
| \[=180{}^\circ \] |
| Then, \[4x+5x+9x=180{}^\circ \] |
| \[\Rightarrow \] \[18x=180{}^\circ \]\[\Rightarrow \]\[x=10{}^\circ \] |
| The smallest angle \[=4\times 10{}^\circ =40{}^\circ \] |
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