Find the measures of the angles of a triangle if the measure of one angle is twice the measure of a second angle and the third angle measures 3 times the second angle decreased by 48.

Step-by-step explanation:

A triangle consists of 3 angles and sides. The sum of the angles in a triangle is 180°. Let the angle be <A, <B and <C.

<A + <B + <C = 180° 1

If the measure of one angle is twice the measure of a second angle then

<A = 2<B 2

Also if the third angle measures 3 times the second angle decreased by 48, this is expressed as <C = 3<B-48 3

Substituting equations 2 and 3 into 1 will give;

(2<B) + <B + (3<B-48) = 180°

6<B- 48 = 180°

add 48 to both sides

6<B-48+48 = 180+48

6<B = 228

<B = 228/6

<B =38°

To get the other angles of the triangle;

Since <A = 2<B  from equation 2;

<A = 2(38)

<A = 76°

Also <C = 3<B-48 from equation 3;

<C = 3(38)-48

<C = 114-48

<C = 66°

Hence the measures of the angles of the triangle are 38°, 66° and 76°

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