Question

If the measure of an exterior angle of a triangle is (3x - 10) and the measure of the interior opposite angles are 25 and (x+15), find and hence the value of all the three angles,​

Answer 1

AnswEr :

$\bold{Given} \begin{cases} \underline{ \footnotesize\sf{ \star \: \: Angles\:of \: a \: Triangle}} \\ \sf{Exterior \: Angle=(3x - 10)\degree} \\ \sf{Interior \: Angle (I_1)=25 \degree} \\ \sf{Interior \: Angle (I_2)=(x +15)\degree}\end{cases}$

• Accrⁿ to the Exterior Angle Theorem :

⇒ Exterior Angle = Sum of Opposite Interior Angles

⇒ Exterior Angle = I₁ + I₂

⇒ (3x - 10) = 25 + (x + 15)

⇒ 3x - 10 = 25 + x + 15

⇒ 3x - x = 40 + 10

⇒ 2x = 50

⇒ x = $\cancel\dfrac{50}{2}$

⇒ $\boxed{ \sf x = 25}$

_________________________________

⋆ Exterior Angle :

» (3x - 10) = (3 × 25 - 10) = (75 - 10) = 65°

⋆ Interior Angle₁ :

» 25°

⋆ Interior Angle₂ :

» (x + 15) = (25 + 15) = 40°

⠀

∴ Angles are 65°, 25° and 40° respectively.

Answer 2

Solution

Given angles are 25°,(3x - 10)° and (x + 15)°

According to Exterior Angle Theorem,

The exterior angle is equal to the sum of opposite interior angles

3x - 10 = (x + 15) + 25

→ 3x - 10 = x + 40

→ 3x - x = 40 + 10

→ 2x = 50

→ x = 25°

Now,

• 3x - 10 = 3(25) - 10 = 75 - 10 = 65°

• x + 15 = 25 + 15 = 40°

Thus,the angles are 40°,25° and 65°