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To find ∠B, we will want to find ∠C. As all of the interior angles of a triangle add up to 180°, we could subtract the measures of angles A and C to find B.

First of all, our 113° angle and ∠C are supplementary. This means that their angle measures add up to 180°. As you can see, combining their angle measures would make a semi-circle, or a straight angle.

113+c=180

We subtract 113 from both sides.

c=67

Therefore, angle c is 67°.

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Now, we need to find ∠B. We know that all of the interior angles equal 180°. This gives us the equation below.

72+67+B=180

139+B=180

B=41

Therefore, [tex] \boxed {\angle B=41} [/tex]°

I hope this helps!

Supernova Supernova · Answer 2 · 2018-08-06T01:00:22+02:00

First you need to find m∠ACB. m∠ACB and m∠DCB form a straight line, so that means they must add up to 180 degrees. Make them add up to 180 in an equation.

m∠ACB + 113 = 180

Subtract 113 from both sides.

m∠ACB = 67

The sum of the measures of the interior angles of a triangle add up to 180 degrees. Make m∠A + m∠B + m∠BCA = 180 in an equation.

72 + m∠B + 67 = 180

Combine like terms.

139 + m∠B = 180

Subtract 139 from both sides.

m∠B = 41°