Question

The three angles the three angles of a triangle are in the ratio 6:3: 1 find all the angles of a triangle

Answer 1

Answer:The measures of the angles of a triangle are in the ratio of 1:3:6. ... Let the smaller angle be = to x, then x + 3x + 6x = 180. Combining like terms yields 10x = 180. Therefore, x = 18 degrees, 3x = 3(18) or 54 degrees, and 6x = 6(18) or 108 degrees.

Step-by-step explanation:

Answer 2

$\huge {\underline {\underline {\bf{\blue{Required \: Answer :}}}}}$

${\underline {\bf{\blue{Given:}}}}$

. ratio of angles of triangle = 6:3:1

${\underline {\bf{\blue{To\: find :}}}}$

. Measure of all angles of triangle

${\underline {\bf{\blue{Explanation:}}}}$

Let the all angles of triangle are as :-

6x°, 3x° and 1x°

Now,

We know that, according to a property of triangle, sum of interior angles of triangle is equal to 180°

So,

by this property of triangle, we can say that 6x°+3x°+1x° = 180°

Let solve it =>

6x°+3x°+1x° = 180°

=> 10x° = 180°

=> x = 180/10

=> x = 18°

By solving this , we foun that the value of x = 18°

Hence,

We can find the measure of all angles of triangle by putting the value of x in its unknown angles.

Let's put the value of x in 6x°+3x°+1x°

. 6x°

=> 6 × 18° = 108°

. 3x°

=> 3×18 = 54

. 1x

=> 1x° ×18 = 18°

Hence,

The measure of all angles of triangle are as :--

108°, 54° and 18°

$\huge { \underline {\bf{\red {Verification:}}}}$

to verify our statement, We have to add all angles of triangle equate it by 180° and have to make LHS = RHS

$let \: do \: it$

108°+54°+18° = 180°

=> 162°+18° = 180°

=> 180° = 180°

LHS = RHS

hence, verified