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basic geometry and measure...
course: basic geometry an_ > unit 11
lesson 2: missing angles problems
find measure of vertical angles
due oct 17, 3:30 pm
finding missing angles
attempted • 43%
finding angle measures between...
not started
note: angles not necessarily drawn to scale.
$x = square^{circ}$

Explanation:

Step1: Use the property of vertical angles and right angles

We know that \( \angle CGB = 90^{\circ}\). The angle adjacent to \(15^{\circ}\) and \(x\) forms a straight - line (sum to \(180^{\circ}\)) considering vertical - angle relationships. Also, we can use the fact that \(x\) and \(15^{\circ}+90^{\circ}\) are supplementary (because of the straight - line formed by \(AF\) and \(BE\) intersecting at \(G\)).
The sum of angles around a point on a straight - line is \(180^{\circ}\). We know that \(x+(90^{\circ}+15^{\circ})=180^{\circ}\) (since \( \angle AGB = 180^{\circ}\) and \( \angle AGC = 90^{\circ}\), and using the angle - addition property).

Step2: Solve for \(x\)

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Answer:

\(75\)