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

ZA and ZB are supplementary angles. If m≤A = (4x + 29)˚ and m ZB = (3x + 11)°, then-example-1

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Answer:


\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°.

______________________

Hope this helps!

Have a great day!

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