Question

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Figure B is a scaled copy of Figure A.

What is the scale factor from Figure A to Figure B?

Answer 1

x = 60°

Explanation:

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The sum of angles on a line is 180°.

Given that Angle G is 90°, the other measure on Line DB would also be 90°. The missing angle next to x can be called y.

• x° + y° = 90°

Angle Y

The Angle y can be calculated by using the Vertical Angles Theorem. The theorem states that if two non-adjacent angles are formed by the intersection of two lines, the measures of the angles are congruent.

This means that the measure of Angle y is 30°, as the 30° angle and y are non-adjacent and are formed by the intersection of lines AC and EF.

Angle X

We can now solve for x by plugging in 30° for y in the equation.

• x° + y° = 90°
• x° + 30° = 90°
• x° = 60°

The value of x is 60°.

Answer 2

Answer: x = 60°

Explanation:

We know a circle is equal to 360°, so we can subtract from 360° to find x using vertical angles and other given details.

Vertical (opposite) angles are equal to each other. This is why, for example, we know AGE and FGC are both 30°.

See attached for a breakdown of the angles.

360° - 30° - 30° - 90° - 90° = 2x

120° = 2x

60° = x