In a right angled triangle, the two acute angles are in the ratio 2:3 find these angles

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In a right angled triangle ; One angle = 90° . We know that ,Sum of angles in a traingle =180° . Given that ratio of other two angles =1:2 . Let the other angles be x,2x. Now ,According to The Angle Sum Property. => x + 2x + 90 = 180 => 3x =90 => x =30 . Therefore ,Now angles are 30° , 60° . If The acute angle of a right triangle are in the ratio 2: 1 , Then the acute angles are 30° , 60° .

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In a right angle triangle, two acute angles are in the ratio 2:3. Find the angles?

Convert each of the following repeating decimals to form, where a and b are integers and : __ a. 0.7 __ C 2.37 __
e 4.34
The two acute angles add up to 90 degrees. Since the ratio is 2:3, divide 90 up into (2+3) parts of 18 degrees each. Thus, the angles are 18*2 = 36 degrees and
18*3 = 54 degrees
In a right angle divided in two angles are in the ratio 2:3.find the each angles.

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In a right angled triangle ; One angle = 90° . We know that ,Sum of angles in a traingle =180° . Given that ratio of other two angles =1:2 . Let the other angles be x,2x. Now ,According to The Angle Sum Property. => x + 2x + 90 = 180 => 3x =90 => x =30 . Therefore ,Now angles are 30° , 60° . If The acute angle of a right triangle are in the ratio 2: 1 , Then the acute angles are 30° , 60° .

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It is given that the two acute angles are in the ratio \[2:3\].Let the two acute angles be \[2x\] and \[3x\] respectively.As we know, the third angle of the triangle is a right angle. Thus, the measure of the third angle is \[90^\circ \].Now, the angle sum property of a triangle states that the sum of the measures of the three interior angles of a triangle is always \[180^\circ \].Thus, the sum of the two acute angles and the right angle will be equal to \[180^\circ \].Therefore, we get\[2x + 3x + 90^\circ = 180^\circ \]We will now solve the equation to find the value of \[x\].Subtracting \[90^\circ \] from both sides of the equation, we get\[\begin{array}{l} \Rightarrow 2x + 3x + 90^\circ - 90^\circ = 180^\circ - 90^\circ \\ \Rightarrow 2x + 3x = 90^\circ \end{array}\]Adding the like terms in the equation, we get\[ \Rightarrow 5x = 90^\circ \]Dividing both sides by 5, we get\[\begin{array}{l} \Rightarrow \dfrac{{5x}}{5} = \dfrac{{90^\circ }}{5}\\ \Rightarrow x = 18^\circ \end{array}\]Therefore, we get the value of \[x\] as \[18^\circ \].Finally, we will substitute the value of \[x\] to find the measures of the two acute angles.Substituting \[x = 18^\circ \] in \[2x\], we get the first acute angle as\[2x = 2 \times 18^\circ = 36^\circ \]Substituting \[x = 18^\circ \] in \[3x\], we get the second acute angle as\[3x = 3 \times 18^\circ = 54^\circ \]

\[\therefore\] The measure of the two acute angles of the right angled triangle are \[36^\circ \] and \[54^\circ \] respectively.

Note: It is given in the question that the triangle is right angled, which means one of the angles of the triangle is \[90^\circ \]. If it was given an equilateral triangle, it means that every angle of the triangle is \[60^\circ \]. We need to also keep in mind that the sum of interior angles of a triangle is \[180^\circ \] and not \[360^\circ \] which is the sum of interior angles of a quadrilateral.

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