Answered

On a piece of paper, use a protractor and a ruler to construct △ABC with AB=8 cm , m∠A=70° , and m∠B=55° . What is AC ?

A)4 cm

B)6 cm

C8 cm

D)12 cm

MAKE SURE YOUR ANSWER IS RIGHT PLEASE!

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JeanaShupp

Answer: C) 8 cm


Step-by-step explanation:

Given: In △ABC  AB=8 cm , m∠A=70° , and m∠B=55° .

The angle sum property of triangle says that the sum of all interior angles in a triangle is equals to 180°.

⇒ m∠A+m∠B+m∠C=180°

⇒70°+55°+m∠C=180°

⇒m∠C=180°-125°

⇒m∠C=55°

Now, in △ABC m∠C= m∠B= 55°

⇒AB=AC [∵ Sides opposite to equal angles of a triangle are equal]

⇒ AC= 8 cm.

Answer:

The correct answer is option (C).

Step-by-step explanation:

Given: ΔABC, ∠A=70° ,∠B=55° , AB = 8 cm

To find: AC=?

Solution:

In ΔABC

∠A + ∠B + ∠C= 180° (Angle sum property of the triangles)

70° + 55° + ∠C= 180°

∠C = 55°

In the ΔABC, ∠B is 55° and ∠C is also 55° which means that sides opposites to these angles will also be equal.

∠C = ∠B = 55°

AB = AC = 8 cm

(In triangle,Sides opposites to the equal angles are equal)

Hence, the correct answer is option (C).

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