Respuesta :
Step-by-step explanation:
Need to FinD :
- We have to find the measures of other two angles of triangle.
[tex] \red{\frak{Given}} \begin{cases} & \sf{The\ measure\ of\ one\ angle\ of\ traingle\ is\ {\pmb{\sf{10^{\circ}}}}.} \\ & \sf{The\ other\ two\ angles\ are\ in\ the\ ratio\ of\ {\pmb{\sf{3\ :\ 14}}}.} \end{cases}[/tex]
We know that,
- The other two angles of triangle are in the ratio of 3 : 14. So, let us consider the other two angles of the triangle be 3x and 14x.
Angle sum property,
- The angle sum property of triangle states that the sum of interior angles of triangle is 180°. By using this property, we'll find the other two angles of the triangle.
[tex]\rule{200}{3}[/tex]
[tex] \sf \dashrightarrow {10^{\circ}\ +\ 3x\ +\ 14x\ =\ 180^{\circ}} \\ \\ \\ \sf \dashrightarrow {10^{\circ}\ +\ 17x\ =\ 180^{\circ}} \\ \\ \\ \sf \dashrightarrow {17x\ =\ 180^{\circ}\ -\ 10^{\circ}} \\ \\ \\ \sf \dashrightarrow {17x\ =\ 170^{\circ}} \\ \\ \\ \sf \dashrightarrow {x\ =\ \dfrac{\cancel{170^{\circ}}}{\cancel{17}}} \\ \\ \\ \dashrightarrow {\underbrace{\boxed{\pink{\frak{x\ =\ 10^{\circ}.}}}}_{\sf \blue {\tiny{Value\ of\ x}}}} [/tex]
∴ Hence, the value of x is 10°. Now, let us find out the other two angles of the triangle.
[tex]\rule{200}{3}[/tex]
Second AnglE :
- 3x
- 3 × 10
- 30°
∴ Hence, the measure of the second angle of triangle is 30°. Now, let us find out the third angle of triangle.
[tex]\rule{200}{3}[/tex]
Third AnglE :
- 14x
- 14 × 10
- 140°
∴ Hence, the measure of the third angle of the triangle is 140°.
