Question

Find m∠DEA if m∠DEA= x + 30, m∠AEF= x + 132, and m∠DEF= 146 degrees

Answer 1

The numerical sum of the degree measures of m ∠DEA and m ∠AEF and  m ∠DEF is 360°; The numerical measures of the angles is,

m ∠DEA = 56°

m ∠AEF = 158°

m ∠DEF = 146°

Based on the given data,

m ∠DEA= x + 30,

m ∠AEF= x + 132, and

m ∠DEF= 146 degrees

If the sum of two linear angles is 360° then, they are known as supplementary angles.

∠A + ∠B + ∠C = 360°, (∠A and ∠B and ∠C are linear angles.)

So,

We can write,

m ∠AEF + m ∠DEA + m ∠DEF = 360°

( x + 132) + (x + 30) + 146  = 360°

x + 30 + x + 132 + 146  = 360°

2x + 308 = 360°

2x = 360° - 308

x = 52/2

x =26

Now, we will substitute the value of x = 26° in the ∠DEA and ∠AEF, hence we get:

m ∠DEA = x + 30

m ∠DEA = 26 + 30

m ∠DEA = 56 degrees

Also,

m ∠AEF = x + 132

m ∠AEF = 26 + 132

m ∠AEF = 158

Hence,

m ∠DEA + m ∠AEF + m ∠DEF = 360°

56 + 158 + 146 = 360°

360° = 360°

Therefore,

Therefore, the numerical sum of the degree measures of m ∠DEA and m ∠AEF and  m ∠DEF is 360°; The numerical measures of the angles is,

m ∠DEA = 56°

m ∠AEF = 158°

m ∠DEF = 146°

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