Question

Lines e and f are parallel. the mangle9 = 80° and mangle5 = 55°. parallel lines e and f are cut by transversal c and d. all angles are described clockwise, from uppercase left. where lines e and c intersect, the angles are: 1, 2, 4, 3. where lines f and c intersect, the angles are 5, 6, 8, 7. where lines e and d intersect, the angles are 9, 10, 12, 11. where lines f and d intersect, the angles are 13, 14, 16, 15. which angle measures are correct? select three options. mangle2 = 125° mangle3 = 55° mangle8= 55° mangle12 = 100° mangle14 = 100°

Answer 1

We can use the properties of parallel lines and transversals to determine the measures of the angles.

From the given information, we know that lines e and f are parallel, and the angles 9 and 80° form a linear pair, which means that angle 9 measures 180° - 80° = 100°.

Similarly, angle 5 and 55° form a linear pair, so angle 5 measures 180° - 55° = 125°.

Using the alternate interior angles property, we know that angles 3 and 8 are congruent, and both are equal to angle 5 - angle 4 = 125° - 80° = 45°. Therefore, option (ii) is incorrect.

Using the corresponding angles property, we know that angles 12 and 6 are congruent, and both are equal to angle 9 + angle 80° = 100° + 80° = 180°. Therefore, option (iv) is correct.

Using the vertical angles property, we know that angles 14 and 2 are congruent, and both are equal to angle 80°. Therefore, option (v) is correct.

Therefore, the correct options are (i) mangle2 = 125°, (iv) mangle12 = 100°, and (v) mangle14 = 100°.