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3 years ago

I need help in these questions

Mathematics

1 answer:

Salsk061 [2.6K]3 years ago

3 0

Answer:

see explanation

Step-by-step explanation:

All of these questions use the external angle theorem, that is

The external angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠3 = 43° + 22° = 65°

∠2 + 71 = 92 ( subtract 71 from both sides )

∠2 = 21°

90 + ∠4 = 123 ( subtract 90 from both sides )

∠4 = 33°

2x - 15 + x - 5 = 148

3x - 20 = 148 ( add 20 to both sides )

3x = 168 ( divide both sides by 3 )

x = 56

Hence ∠ABC = x - 5 = 56 - 5 = 51°

2x + 27 + 2x - 11 = 100

4x + 16 = 100 ( subtract 16 from both sides )

4x = 84 ( divide both sides by 4 )

x = 21

Hence ∠JKL = 2x - 11 = (2 × 21) - 11 = 42 - 11 = 31°

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