Question

1. a ladder is against a building. the angle it makes with the ground is twice the angle it makes with the building. what is the measure of the exterior angle formed between the ground and the ladder?

Explanation:

Step1: Define angles

Let the angle the ladder makes with the building be $x$. Then the angle it makes with the ground is $2x$.

Step2: Use angle - sum property

Since the building is perpendicular to the ground, $x + 2x=90^{\circ}$ (the sum of the two non - right angles in the right - triangle formed by the ladder, building and ground).

Step3: Solve for $x$

Combining like terms, we have $3x = 90^{\circ}$. Dividing both sides by 3 gives $x = 30^{\circ}$, and $2x=60^{\circ}$.

Step4: Find the exterior angle

The exterior angle to the angle between the ground and the ladder is supplementary to the angle between the ground and the ladder. The angle between the ground and the ladder is $60^{\circ}$, so the exterior angle is $180^{\circ}-60^{\circ}=120^{\circ}$.

Answer:

$120^{\circ}$