Question

Triangle ghj has the exterior angles shown below. triangle g h j. the exterior angles are (9 x 6) degrees, (10 x 7) degrees, (10 x minus 1) degrees. for triangle g h j, what is the value of x? 2.7 5.8 12 29

Answer 1

The sum of all the angles of a triangle is equal to 180°. The value of x is 12.

What is the sum of all the angles of a triangle?

The sum of all the angles of a triangle is equal to 180°.

What is the exterior angle?

The Exterior Angle is the angle formed by either of a shape's sides and a line drawn from the opposite side.

We know that in a triangle the sum of the exterior angle and the interior angle is 180°. Therefore, the following angles of the triangle can be written as,

$\angle H=180-(9x+6)$

$\angle G=180-(10x-1)$

$\angle J=180-(10x+7)$

Now, the sum of all the angles of the triangle is 180°, therefore, the sum can be written as,

$\angle H+\angle G+\angle J=180^o\\\\180-(9x+6) + 180-(10x-1) + 180-(10x+7) = 180\\\\540-(9x+6)-(10x-1)-(10x+7)=180\\\\540-180 = (9x+6)+(10x-1)+(10x+7)\\\\360=9x+6+10x-1+10x+7\\\\360=29x+12\\\\360-12=27x\\\\x = 12$

Hence, the value of x is 12.

Learn more about Exterior Angle:

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Answer 2

Answer:

12

Step-by-step explanation: