Answer:
(a) ∠7 = 47°. Angles 5 and 7 are vertical angles, hence congruent.
(b) 47 +(2x -5) = 180
(c) 69
Explanation:
Given angles identified as ∠5, ∠6, ∠7 where two lines cross, and the measure of ∠5 as 47°, you want the measure of ∠7, and an equation and solution when ∠6 is (2x-5).
(a) Vertical angles
Angles that share a vertex and are formed from opposite rays are "vertical angles." They are congruent.
Angles 5 and 7 are vertical angles, so the measure of angle 7 is the same as the measure of angle 5.
∠7 = 47°
(b) Supplementary angles
Angles that form a linear pair are supplementary. This means the sum of angles 5 and 6 is 180°.
∠5 +∠6 = 180°
47° +(2x -5)° = 180°
(c) Solution
2x = 138 . . . . . . . . . . . . divide by °, subtract 42
x = 69