Question

what is the value of h?
$h = 20$
$h = 35$
$h = 55$
$h = 70$
$(2h)^{circ}$
$(2h)^{circ}$

Explanation:

Step1: Use the exterior angle sum property

The sum of exterior angles of a polygon is \(360^{\circ}\). For a triangle, if the exterior angles are \(2h\), \(2h\) and \(40 + 180-(2h)\) (but using the general exterior - angle sum formula for any polygon which is \(360^{\circ}\)). The formula for the sum of exterior angles of a polygon is \(360^{\circ}\). Here, we have \(2h+2h+(180 - 40)=360\) (using the linear - pair relationship to relate the interior and exterior angles). Simplifying, \(2h+2h + 140=360\).

Step2: Combine like terms

Combine the \(h\) terms: \(4h+140 = 360\).

Step3: Isolate the variable term

Subtract 140 from both sides: \(4h=360 - 140\), so \(4h=220\).

Step4: Solve for \(h\)

Divide both sides by 4: \(h=\frac{220}{4}=55\).

Answer:

\(h = 55\) (the third option)