Question

ZA and ZB are supplementary angles. If m≤A = (4x + 29)˚ and m ZB = (3x + 11)°, then find the measure of ZB.​

Answer 1

`\boxed{\sf m\angle B=71^o}`

Explanation:

For the two angles, ∠A & ∠B, to be supplementary angles,

m∠A + m∠B = 180°

Here:-

• 
  `\sf m\angle A=(4x + 29)^o`

• 
  `\sf m\angle B=(3x + 11)^o`

Thus,

`\sf (4x + 29) + (3x + 11)=180^o`

`\sf 4x+29+3x+11=180^o` (Combine like terms)

`\sf 7x+40=180^o` (Subtract 40 from both sides)

`\sf 7x+40-40=180-40`

`\sf 7x=140` (Simplify)

`\sf \cfrac{7x}{7}=\cfrac{140}{7}` ( Divide both sides by 7)

`\boxed{\bf x=20}`

Now that we know what x is, let's find the measure of ∠B:-

`\sf m\angle B=(3x+11)`

`\sf 3(20)+11` ( Multiply:- 3 × 20 = 60)

`\sf 60+11` (Add)

`\boxed{\bf 71^o}`

Therefore, the measure of ∠B = 71°.

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Hope this helps!

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