Question

Point G lies outside of circle F. There are two tangent lines that intersect outside circle F at point G. They intersect circle F at

points H and J.
Use the information provided to complete the statement. Type the correct answer in the box. Use numerals instead of words.
If m/HGJ = 27°, then m/HFJ is

Answer 1

To find the measure of angle HFJ, subtract the given angle from 180°.

Step-by-step explanation:

To find the measure of Κ/HFJ, we can use the fact that tangent lines are perpendicular to the radius drawn to the point of tangency. In this case, GHJ is a right triangle, with HG as the hypotenuse and HF as one of the legs. Since the tangent and radius are perpendicular, we know that measure of ΚGHJ = 90°.

The sum of the angles in a triangle is 180°, so we can find measure of ΚHFJ by subtracting the given angle from 180°. Therefore, m/HFJ = 180° - m/HGJ = 180° - 27° = 153°.

Learn more about Triangle angles