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

Answer:

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

Step-by-step 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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