Question

in a triangle ABC, a b equals to AC and angle A : b equals to 8: 5 find angle A​

Answer 1

ab = ac

angle b : angle b = 8:5

let them be 8x , 5x

angle b = angle c

angles opposite to equal sides are equal

now

angle a + angle b + angle c = 180

8x + 5x + 5x = 180

18x = 180

x = 10

now angle a = 8x = 80

Answer 2

Given,

In a triangle $ABC$, $AB$ equals to $AC$ and $A:B$ equals to $8:5$

Here, we have to find the angle of $A$

According to the question,

$AB=AC$

So,

Angle $B$ $=$ Angle $C$    (From, opposite angles to equal sides are equal)

$A:B=8:5$

Let, angles be $8x,5x$

Angle $B$ $=$ Angle $C$  $= 5x$

We know that,

The sum of angles of a triangle is equal to $180$ degrees.

$8x+5x+5x=180$

$18x=180$

$x=10$

Substitute $x=10$ in $8x$

Angle $A=8x=8\times10=80$

Therefore, the value of angle $A$ is $80^{0}$.