Question

Examine the figures below.
If ΔABC is similar to ΔDEF, determine the measure of ∠A
Options below:
A. 16°
B. 22°
C. 33°
D. 66°

Answer 1

Answer:

The correct option is C. 33°

Step-by-step explanation:

Similarity

Triangles with the same shape but different sizes are said to be similar triangles.  In other words, two triangles that are comparable have corresponding sides that are proportionately equal and corresponding angles that are congruent. Similar Triangle is indicated here by the symbol "~".

Conditions of Similar Triangles

Angle-Angle Similarity, abbreviated AA (or AAA),

The two triangle is said to be similar if any two angles of its three angles of  a triangle are equal to any two of its three angles of another triangle.

Side-Angle-Side Similarity, or SAS

Two triangles are said to be similar triangles if their two sides are in the same ratio as the two sides of another triangle and their two sides' angles inscribed in both triangles are equal.

Side-Side-Side Similarity, or SSS

The two triangles are similar triangles if all three sides of one triangle are in proportion to the three sides of another triangle.

Explanation of the above answer,

According to the above Question,

As it is mentioned in the question that the triangles are similar.

∵ In similar triangles, the corresponding sides are in proportion,

∴ ΔABC ~ ΔDEF

     ⇒    $\frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF}$

     ⇒   $\frac{AB}{DE} = \frac{AC}{DF}$  

    ⇒    $\frac{12}{8} = \frac{9}{6}$

    ⇒    $\frac{3}{2} = \frac{3}{2}$

∵ the sides are proportion

∴ The angles between the sides are equal.

⇒       ∠BAC = ∠EDF

⇒       3x-33 = x+11

⇒        2x = 44

⇒        x = 22

∴       ∠A = 3x - 33 = 3 × 22 - 33 = 33°

Hence, the correct option is Option C. 33    

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