Question

the measures of accute angle of a right angled triangle are y and 2y. find these two angles?​

Answer 1

Answer:

30° & 60°

Step-by-step explanation:

As per the provided information in the given question, it has been stated that the measures of acute angle of a right-angled triangle are y and 2y. We have,

• The measures of acute angle of a right-angled triangle are y and 2y.

We are asked to calculate the the measure of two angles.

― As it is known to us that, sum of all the interior angles of a triangle is 180°. Since it is a right- angled triangle, so measure of one angle will be 90°. Thus now,

⠀⠀⠀★ 1st angle = y

⠀⠀⠀★ 2nd angle = 90°

⠀⠀⠀★ 3rd angle = 2y

Now, according to the angle sum property of the triangle,

$\longrightarrow \sf{\quad { y + 90^\circ + 2y = 180^\circ}}$

Performing the addition of the like terms.

$\longrightarrow \sf{\quad { 90^\circ + 3y = 180^\circ}}$

Transposing 90° from L.H.S to R.H.S, its sign will get changed.

$\longrightarrow \sf{\quad { 3y = 180^\circ - 90^\circ}}$

Performing subtraction in R.H.S.

$\longrightarrow \sf{\quad { 3y = 90^\circ}}$

Now, transposing 3 from L.H.S to R.H.S, its arithmetic operator will get changed.

$\longrightarrow \sf{\quad { y =\cancel{\dfrac{ 90^\circ}{3}} }}$

Dividing 90 by 3.

$\longrightarrow \quad {\textbf{\textsf{ y = 30}}^\circ}$

Now, we have to find the value of both acute angles.

$\longrightarrow \sf{\quad {Acute \;angle_{(1st)} = y }}$

Substitute the value of y.

$\longrightarrow \quad\underline{\boxed {\textbf{\textsf{Acute \;angle}}_{\textbf{\textsf{(1st)}}} = \textbf{\textsf{30}}^\circ} }$

Also,

$\longrightarrow \sf{\quad {Acute \;angle_{(2nd)} = 2y }}$

Substitute the value of y.

$\longrightarrow \sf{\quad {Acute \;angle_{(2nd)} = 2(30)^\circ }}$

Performing multiplication.

$\longrightarrow \quad\underline{\boxed {\textbf{\textsf{Acute \;angle}}_{\textbf{\textsf{(2nd)}}} = \textbf{\textsf{60}}^\circ} }$

$\underline{ \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$

Therefore,

⠀⠀⠀★ Acute angles = 30° & 60°