Question

A triangle with exterior angles is shown. A triangle sits on a line and forms 2 exterior angles on the left and right of the triangle of (2 h) degrees. The top interior angle of the triangle is 40 degrees. What is the value of h? h = 20 h = 35 h = 55 h = 70

Answer 1

Answer:

Option 3.

Step-by-step explanation:

It is given that a triangle sits on a line and forms 2 exterior angles on the left and right of the triangle of (2h) degrees.

The top interior angle of the triangle is 40 degrees.

$\angle BAC=40$

From the given figure it is clear that

$\angle ABC+2h=180$               (Supplementary angle)

$\angle ABC=180-2h$

$\angle ACB+2h=180$               (Supplementary angle)

$\angle ACB=180-2h$

According to the angle sum property of triangle, the sum of all interior angles of a triangle is 180 degree.

$\angle ABC+\angle ACB+\angle BAC=180$

$(180-2h)+(180-2h)+40=180$

Combine like terms.

$(180+180+40)+(-2h-2h)=180$

$400-4h=180$

$-4h=180-400$

$-4h=-220$

Divide both sides by -4.

$h=\frac{-220}{-4}$

$h=55$

The value of h is 55.

Therefore, the correct option is 3.

Answer 2

Answer:

option 3

Step-by-step explanation:

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