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Vera_Pavlovna [14]
3 years ago
13

In triangle ABC, angle A = 2x°, angle B = (x-45)° and angle C = (x-15)°.

Mathematics
1 answer:
Lelechka [254]3 years ago
5 0
Sum\ of\ angles\ in\ triangle\ is\ equal\ to\ 180^{\circ}\\\\
To\ find\ x\ sum\ all\ angles:\\
2x+x-45+x-15=180\\\\
4x-60=180\ \ \ |Add\ 60\\\\
4x=60+180\\\\
4x=240\ \ \ |Divided\ by\ 4\\\\
x=60^{\circ}\\\\
\angle \  A=2x=2*60=120^{\circ}\\
\angle\ B=x-45=60-45=15^{\circ}\\
\angle\ C=x-15=60-15=45^{\circ}\\\\Triangle\ is\ \textbf{obtuse}.
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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
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