$\red{\frak{Given}} \begin{cases} & \sf{The\ measure\ of\ one\ angle\ of\ traingle\ is\ {\pmb{\sf{10^{\circ}}}}.} \\ & \sf{The\ other\ two\ angles\ are\ in\ the\ ratio\ of\ {\pmb{\sf{3\ :\ 14}}}.} \end{cases}$

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.

$\rule{200}{3}$

$\sf \dashrightarrow {10^{\circ}\ +\ 3x\ +\ 14x\ =\ 180^{\circ}} \\ \\ \\ \sf \dashrightarrow {10^{\circ}\ +\ 17x\ =\ 180^{\circ}} \\ \\ \\ \sf \dashrightarrow {17x\ =\ 180^{\circ}\ -\ 10^{\circ}} \\ \\ \\ \sf \dashrightarrow {17x\ =\ 170^{\circ}} \\ \\ \\ \sf \dashrightarrow {x\ =\ \dfrac{\cancel{170^{\circ}}}{\cancel{17}}} \\ \\ \\ \dashrightarrow {\underbrace{\boxed{\pink{\frak{x\ =\ 10^{\circ}.}}}}_{\sf \blue {\tiny{Value\ of\ x}}}}$

∴ Hence, the value of x is 10°. Now, let us find out the other two angles of the triangle.

$\rule{200}{3}$

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.

$\rule{200}{3}$

Third AnglE :

14x
14 × 10
140°

∴ Hence, the measure of the third angle of the triangle is 140°.

5 0

2 years ago

Find the slope of the line passing through the point (-3, 6) and the origin.<br> M=

Nuetrik [128]

You know b=0 because it is passing through the orgin (0,0) and b is the y intercept. You input (-3,6) as (x,y)

7 0

3 years ago