The second angle of a triangle is twice the first angle. The third angle is 20 degrees more than the first angle. What is the first angle?

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The second angle of a triangle is twice the first angle. The third angle is 20 degrees more than the first angle. What is the first angle?

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Answer 1 · 2015-12-08T14:12:38

A1=40

Explanation:

Let A1,A2,A3 be the angles of the triangle

We know, A1+A2+A3 = 180 -------(1)
given A2=2(A1) ------(2)
A3= A1+20 --------(3)

Putting 2 & 3 in 1 , we get

A1+2(A1)+A1+20=180

$\Rightarrow 4 (A 1) = 160$ $=>4(A1)=160$

A1=40

Answer 2 · 2015-12-08T14:26:01

$40$ $40$

Explanation:

Let x be first interior angle of the triangle. Then, second and third interior angles will be $2 x$ $2x$ and $x + 20$ $x+20$ , respectively.

The sum of the measures of the interior angles of a triangle is 180 degrees:
$\times x + 2 x + x + 20 = 180$ $color(white)(xx)xcolor(blue)(+)2xcolor(blue)(+)x+20=180$
$\Rightarrow 4 x + 20 = 180$ $=>4x+20=180$
$\Rightarrow 4 x + 20 - 20 = 180 - 20$ $=>4x+20color(red)(-20)=180color(red)(-20)$
$\Rightarrow \frac{1}{4} \cdot 4 x = \frac{1}{4} \cdot 160$ $=>color(red)(1/4*)4x=color(red)(1/4*)160$

$\Rightarrow x = 40$ $=>x=40$

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The second angle of a triangle is twice the first angle. The third angle is 20 degrees more than the first angle. What is the first angle?

2 Answers

Explanation:

Explanation:

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