Question

find the value of x​

Answer 1

Answer:

Hey buddy !

In the triangle ,

6x + (180-9x) + (180-9x) = 180

360 - 12x = 180

180 = 12x

X = 180/12 = 15°

Answer 2

Question:

Find the value of x .

Answer:

x = 15°

Note:

• Angle sum property of a triangle : The sum of all the three angles of a triangle is equal to 180° .

• Exterior angle property of a triangle : The exterior angle of a triangle is equal to the sum of two opposite interior angles .

• Linear pair of angles : Two adjacent angles are said to be linear pair if they lie on the same straight line. Also, linear pairs of angles are supplementary.

• Complementary angles : Two angles are said to be complementary, if their sum is 90° .

• Supplementary angles : Two angles are said to be supplementary, if their sum is 180° .

Solution:

First of all , let's name the vertices of the triangle and the base line .

Thus,

Angle BAC = 6x

Angle ABP = 9x

Angle ACQ = 9x

Also,

=> Angle ABP + Angle ABC = 180° {linear pair}

=> Angle ABC = 180° - Angle ABP

=> Angle ABC = 180° - 9x

For the ∆ABC ,

Angle ACQ is the exterior angle and the two opposite interior angles corresponding to it are Angle ABC and Angle BAC .

Thus,

According to the exterior angle property of a triangle, we have ;

=> Angle ACQ = Angle ABC + Angle BAC

=> 9x = (180° - 9x) + 6x

=> 9x = 180° - 3x

=> 9x + 3x = 180°

=> 12x = 180°

=> x = 180°/12

=> x = 15°

Hence,

Required value of x is 15° .