3 years ago

What is value of x? Enter your answer in the box. x =

Mathematics

1 answer:

Maslowich3 years ago

8 0

Answer:

x = 10

Step-by-step explanation:

Since the line from A is an angle bisector the following ratios are equal

$\frac{AB}{AC}$ = $\frac{x+4}{2x+1}$ , that is

$\frac{8}{12}$ = $\frac{x+4}{2x+1}$ ( cross- multiply )

8(2x + 1) = 12(x + 4) ← distribute both sides )

16x + 8 = 12x + 48 ( subtract 12x from both sides )

4x + 8 = 48 ( subtract 8 from both sides )

4x = 40 ( divide both sides by 4 )

x = 10

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In triangle ABC, angle A is 75o and angle B is 20o. Select the triangle that is similar to triangle ABC.

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A. $\triangle$ DEF where $\angle D = 75^{\circ}$ and $\angle E = 20^{\circ}$ .

Step-by-step explanation:

At first we must keep in mind that two triangles are similar when they have same angle configuration, that is, each pair of angles is congruent. If $\triangle$ ABC and $\triangle$ DEF, then $\angle A \equiv \angle D$ and $\angle B \equiv \angle E$ . Hence, $\angle D = 75^{\circ}$ and $\angle E = 20^{\circ}$ .