Question

1. gate a gate has a diagonal support. describe the relationship between ∠1 and ∠2. 1. pizza mary beth and clem each have a piece of pizza. what is the relationship between the angles of their pieces of pizza?

Explanation:

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Step1: Recall angle - pair relationship in a rectangle

In a rectangle (assuming the gate is rectangular), the diagonal divides the rectangle into two right - angled triangles. $\angle1$ and $\angle2$ are alternate interior angles.

Step2: Apply the property of alternate interior angles

When a transversal (the diagonal) intersects two parallel lines (the sides of the rectangle), alternate interior angles are congruent. So $\angle1=\angle2$.

Step1: Add the two given angles

We have two angles of the pizza slices, $105^{\circ}$ and $75^{\circ}$. Calculate $105 + 75$.
$105+75 = 180^{\circ}$

Step2: Determine the angle relationship

Since the sum of the two angles is $180^{\circ}$, the angles are supplementary.

Answer:

$\angle1$ and $\angle2$ are congruent.

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