Question

State which of the two angles has a greater measure. Refer to the following figures.

Answer 1

Given :    different figures

To Find :  which of the two mentioned  angles has a greater measure.  

Solution:

in first triangle two sides are 8 and one side is 10

Angle opposite to side 8 are equal and angle opposite to 10 is largest hence

∠B > 60°

in second triangle all sides equal hence all angles 60°

=> ∠E = 60°

=> ∠B  > ∠E

∠RAE = ∠DAY  ( vertically opposite angles)

∠GDF > ∠EDF

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Answer 2

we know that, angle opposite to greater side is greater in measure .

so,

1) we have,

• ∠B = opposite to AC = 10
• ∠E = opposite to DF = 8
• 10 > 8 .

therefore,

• ∠B > ∠E .

2) we have,

• ∠EDF = opposite to EF = 19
• ∠GDF = opposite to GF = 20
• 20 > 19

therefore,

• ∠GDF > ∠EDF .

3) we have,

• ∠RAE = opposite to = x
• ∠DAY = opposite to = 2x - 2
• since 5 = x + 2 => x = 3
• then, 2x - 2 = 2*3 - 2 = 4
• 4 > 3.

therefore,

• ∠DAY > ∠RAE .

4) we have,

• ∠R = opposite to = x + 6
• ∠C = opposite to GF = 3x - 6

here , value of x is not given . therefore we can not determine the result .

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