Question

in a right angle triangle one of the acute angle exist exceeds The Other by 20 degree find the measure of both the acute angle in the right angle triangle​

Answer 1

$\mathfrak{\large{\underline{\underline{Answer:-}}}}$

One acute angle = 35°

Another acute angle = 55°

$\mathfrak{\large{\underline{\underline{Explanation-}}}}$

Given :-

In a Right angled triangle

One of the acute angle exceeds the other by 20°

To find :- Measure of two acute angles

Solution :-

We know that In a Right angled triangle one measure will be 90°

So one angle = 90°

Let one of the acute angle be x°

Given that another acute angle exceeds the other by 20°

[Exceeds is nothing but more than]

So, another acute angle = 20° more than x° = (x + 20)°

By Angle sum property of a triangle:-

Equation formed: $\boxed{\tt{x + (x + 20) + 90 = 180}}$

$\tt{\implies{x + x + 20+ 90 = 180}}$

$\tt{\implies{2x + 110 = 180}}$

$\tt{\implies{2x= 180 - 110}}$

$\tt{\implies{2x=70}}$

$\tt{\implies{x = \dfrac{70}{2} }}$

$\tt{\implies{x =35}}$

So one acute angle = 35°

Another acute angle = (x + 20)° = (35 + 20)° = 55°

$\mathfrak{\large{\underline{\underline{Verification:-}}}}$

$\tt{x + (x + 20) + 90 = 180}$

$\tt{\implies{35 + 55 + 90 = 180}}$

$\tt{\implies{90 + 90 = 180}}$

$\tt{\implies{180 = 180}}$