Question

Construct a triangle with AB=7.4 cm angle BAC=47° and angle ABC=68° and find the measure of the third angle to check the accuracy of your construction​

Answer 1

Answer:

BAC + ∠ACB = 100

No information about 3rd angle (insufficient)

2) ∠BAC + ∠ABC = 120

No information about 3rd angle (insufficient)

Statement 1&2: add both equations

∠BAC + ∠ACB = 100 ----------(1)

∠BAC + ∠ABC = 120 ----------(2)

=> 2∠BAC + ∠ACB + ∠ABC = 220 ---------(3)

Also, interior angles of triangle ∠BAC + ∠ACB + ∠ABC = 180 -------------(4)

Equating 3&4 equation.

2∠BAC + ∠ACB + ∠ABC = 220

∠BAC + ∠ACB + ∠ABC = 180

∠BAC = 40

∠ACB = 60

∠ABC = 80

None of the three angles is 90°

Hence ABC is not a right angle triangle.

(Sufficient)

Answer is C