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The sum of the interior angles of a triangle is 180˚, The second angleof a triangle is 45˚ more than the first and the third angle is twice thefirst.

User AlexWien
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1 Answer

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Step-by-step explanation:

The sum of interior angles of a triangle is


180^0

Let the first angle be represented as


x

The second angle of a triangle is 45˚ more than the first

This will be represented below as


x+45

The third angle is twice the first.

This will be represented below as


2x

To figure out the value of the angles, we were given that the sum of angles in the tirangle is 180

Hence,

We will have the expression represented below as


\begin{gathered} x+(x+45)+2x=180^0 \\ firstangle+secondangle+thirdangle=180^0 \end{gathered}

By collecting similar terms, we will have


\begin{gathered} x+(x+45)+2x=180^0 \\ x+x+2x+45=180^0 \\ 4x+45=180^0 \\ substract\text{ 45 from both sides, we will have} \\ 4x+45-45=180-45 \\ 4x=135^0 \\ divide\text{ both sides by 4} \\ (4x)/(4)=(135)/(4) \\ x=33.75^0 \\ secondangle=x+45=33.75+45=78.75 \\ thirdangle=2x=2*33.75=67.5^0 \end{gathered}

Hence,

The final answers are


\begin{gathered} first\text{ }angle=33.75^0 \\ second\text{ }angle=78.75^0 \\ third\text{ }angle=67.5^0 \end{gathered}

User Dnyan Waychal
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