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The sum of the measures of the angles of any triangle is 180 degrees. In triangle
ABC, angles
A and
B have the same measure, while the measure of angle
C is 72 degrees larger than each of
A and
B. What are the measures of the three angles?
Angle
A is
◻ degrees.

The sum of the measures of the angles of any triangle is $180$ degrees. In triangle $A B C$ , angles $A$ and $B$ have the same measure, while the measure of angle $C$ is $72$ degrees larger than each of $A$ and $B$ . What are the measures of the three angles? $\newline$ Angle $A$ is $\square$ degrees.

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Find missing angles in triangles using ratios

Full solution

Q. The sum of the measures of the angles of any triangle is

180

degrees. In triangle

A B C

, angles

A

and

B

have the same measure, while the measure of angle

C

is

72

degrees larger than each of

A

and

B

. What are the measures of the three angles?

\newline

Angle

A

is

\square

degrees.

Define Angles A and B: Let's call the measure of angles A and B $x$ degrees. Since angle C is $72$ degrees larger than each of A and B, we can express angle C as $x + 72$ degrees.
Sum of Triangle Angles: Now, we know that the sum of the angles in a triangle is $180$ degrees. So, we can write the equation: $x + x + (x + 72) = 180$ .
Simplify Equation: Simplify the equation: $3x + 72 = 180$ .
Isolate Variable Term: Subtract $72$ from both sides to isolate the variable term: $3x = 180 - 72$ .
Calculate Value of x: Calculate the right side: $3x = 108$ .
Find Angle C: Divide both sides by $3$ to solve for x: $x = 108 \div 3$ .
Calculate Angle C: Calculate the value of $x$ : $x = 36$ degrees. So, angles $A$ and $B$ are each $36$ degrees.
Calculate Angle C: Calculate the value of $x$ : $x = 36$ degrees. So, angles $A$ and $B$ are each $36$ degrees.Now, let's find the measure of angle $C$ by adding $72$ to the measure of angle $A$ or $B$ : Angle $C = 36 + 72$ .
Calculate Angle C: Calculate the value of $x$ : $x = 36$ degrees. So, angles $A$ and $B$ are each $36$ degrees.Now, let's find the measure of angle $C$ by adding $72$ to the measure of angle $A$ or $B$ : Angle $C = 36 + 72$ .Calculate the measure of angle $C$ : Angle $x = 36$ $1$ degrees.

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