0.8 rrianglesDate10, ind the range of Nothe length for AB,Solve for mAB.mAB<5+9→mABmAB>9−5→mAB50 the length for AB is between 4cm and 14cm, or 4cm<mAB<14cm.Qlsoify each triangle by angles and sides.01.3.4. obtuse triangle scalene triangle The measure of two of the three angles of a triangle are given. Find the neasure of the remaining angle. Then classify the triangle by its angles.: 26. 3,7. 4,8. 5,6 sute triangle ilar pes the9. 0,10. 1,11. 2,12. 3,
Q. 0.8 rrianglesDate10, ind the range of Nothe length for AB,Solve for mAB.mAB<5+9→mABmAB>9−5→mAB50 the length for AB is between 4cm and 14cm, or 4cm<mAB<14cm.Qlsoify each triangle by angles and sides.01.3.4. obtuse triangle scalene triangle The measure of two of the three angles of a triangle are given. Find the neasure of the remaining angle. Then classify the triangle by its angles.: 26. 3,7. 4,8. 5,6 sute triangle ilar pes the9. 0,10. 1,11. 2,12. 3,
Range of mˉAB: First, let's solve for the range of mˉAB. Using the inequalities given: mˉAB<5+9 and mˉAB>9−5.
Upper limit calculation: Calculate the upper limit:5+9=14.So, mˉAB<14 cm.
Lower limit calculation: Calculate the lower limit:9−5=4.So, mˉAB>4 cm.
Combine inequalities for mAB: Combine the two inequalities to get the range for mAB:4cm<mAB<14cm.
Classification of first triangle: Now, let's classify the triangles by angles.For the first triangle with angles 30∘ and 65∘:180∘−(30∘+65∘)=85∘.
Third angle calculation for first triangle: The sum of angles in a triangle is 180°, so the third angle is 85°. This makes it an acute triangle since all angles are less than 90°.
Classification of second triangle: For the second triangle with angles 73° and 37°: 180°−(73°+37°)=70°.
Third angle calculation for second triangle: The sum of angles in a triangle is 180∘, so the third angle is 70∘. This also makes it an acute triangle.
Classification of third triangle: For the third triangle with angles 60° and 60°: 180°−(60°+60°)=60°.
Third angle calculation for third triangle: The third angle is also 60∘, making this an equilateral triangle, which is a special case of an acute triangle.
Classification of fourth triangle: For the fourth triangle with angles 108° and 32°:180°−(108°+32°)=40°.
Third angle calculation for fourth triangle: The third angle is 40∘, and since one angle is greater than 90∘, this is an obtuse triangle.
Classification of fifth triangle: For the fifth triangle with angles 56° and 19°:180°−(56°+19°)=105°.
Third angle calculation for fifth triangle: The third angle is 105∘, which makes this an obtuse triangle as well.
Classification of sixth triangle: For the sixth triangle with angles 30∘ and 30∘: 180∘−(30∘+30∘)=120∘.
Classification of sixth triangle: For the sixth triangle with angles 30∘ and 30∘: 180∘−(30∘+30∘)=120∘.The third angle is 120∘, which is an error because the sum of the first two angles already exceeds 180∘.