Determine if the following problems can construct a triangle given the following information . If the answer is no explain.

Question

A) three angle measures : 22,140,18 degrees

b) three side lengths :17,10,21 inches

c)three angle measures :72,92,46 degrees 

d) two side lengths : 8,4 meters ; include angle :82 degrees

E)three angle measures : 55,67,58 degrees

f)three side lengths :5,7,15 inches

 

Answer 1

Keep in mind the triangle rule: the sum of the measures of the 3 angles of any triangle will equal 180 degrees. Three sides of any length can make a triangle, as long as the triangle is not restricted by an angle of a certain measure.

A. Yes, the sum of the 3 angles is 180 degrees;

B. Yes, any three sides can make a triangle;

C. No, the sum of these angles' measures exceeds 180 degrees;

D. Yes, as these 2 sides are restricted only by a single angle of a particular measure. This angle could be between these 2 sides or opposite the 8 meter side. The angle opposite the 4 meter side must be a smaller angle, as the 4 meter side would not be long enough to reach a side adjacent to the 82 degree angle;

E. Yes, the sum of these angles equals 180 degrees;

F. Yes, again, 3 side lengths unrestricted by angle measurements.

I hope this helps!