9514 1404 393
Answer:
- 52°: angles 4, 13, 18
- 128°: angles 1, 3, 14, 17
- 44°: angles 5, 12, 15
- 136°: angles 2, 6, 11, 16
- 84°: angles 7, 10
- 96°: angles 8, 9
Step-by-step explanation:
Where a transversal (t or u) crosses parallel lines (m and n), there are four angles formed at each intersection. Corresponding and vertical angles are congruent.
Angles in a linear pair are always supplementary. Of course, the angles interior to a triangle always total 180°. These facts let you find the relationships of all the angles in the figure.
Angle 13 corresponds to the given angle 52°, so has the same measure. Angles 4 and 18 are vertical angles with respect to those, so also have the same measure. Angles 1 and 3, 14 and 17 are supplementary to the ones just named, so all have measure 128°.
In the same way, angles on the other side of the figure can be found from the one marked 44°. Angles 5, 12, and 15 also have that measure; and angles 2, 6, 11, and 16 are supplementary, 136°. Angles 7 and 10 finish the triangle interior so that its sum is 180°. That means they are 180° -52° -44° = 84°. Of course, angles 8 and 9 are the supplement of that value, 96°.
In summary:
- 52°: angles 4, 13, 18
- 128°: angles 1, 3, 14, 17
- 44°: angles 5, 12, 15
- 136°: angles 2, 6, 11, 16
- 84°: angles 7, 10
- 96°: angles 8, 9
Answer:
x = -2
Step-by-step explanation:
1/3(x - 10) = - 4
1/3x - 10/3 = - 4
1/3x = -4 + 10/3
1/3x = -2/3
x = -2/3 · 3
x = -2
Answer:
-1.8, -2.1, -2.5, -2.7
Step-by-step explanation:
the bigger the negative number, the smaller it is
Answer:
$108
Step-by-step explanation:
1 box = $12
18 boxes = 12×18 = $216
Total = 18×65 = 1170 pens
Cost price, Cp = $216
3 = $1
378 = 378/3 = $126
1170-378= 792 pens remaining
4 = $1
792 = 792/4 = $198
Total selling price, sp = 126+198 = $324
Profit = Sp - Cp = 324 - 216 = $108
Total marbles : 33
W + G marbles : 11
Probability of picking either a W or G : 11/33
Number of W or G marbles = 11/33 × 45 = 15
