Question

in triangle abc <b =90° and ab = bc then find < a​

Answer 1

Answer : < a = 45°

Explanation : As in ∆abc < b = 90° and ab = bc therefore it is a right angled isoceles triangle which means one angle is 90° and the sides containing that angle are equal.

Now, angles opposite to equal sides are equal and vice versa.

As ab = ac therefore < a = < c,

now by angle sum property,

< a + < b + < c = 180°

x + 90° + x = 180°

2x + 90° = 180°

2x = 90°

x = 45°

Therefore < a = 45°

Answer 2

Measure of $\angle a =45\°$

Step-by-step explanation:

Given:

Δ abc

$ab = bc$

$\angle b= 90\°$

We need to find the $\angle a$

Solution:

Let the  $\angle a$ be $x\°$

Now Given that;

$ab = bc$

and $\angle b= 90\°$

so we can say that;

Δ abc is an isosceles right angled triangle.

so we can say that;

$\angle a=\angle c =x\°$

Now by triangle property we can say that;

Sum of the measures of all angles of the triangle are 180°.

framing in equation form we get;

$\angle a +\angle b+\angle c = 180\°$

Substituting the values we get;

$x+90+x=180\\\\2x+90=180$

Subtracting both sides by 90 we get;

$2x+90-90=180-90\\\\2x=90$

Dividing both side by 2 we get;

$\frac{2x}{2}=\frac{90}{2}\\\\x=45\°$

Hence $\angle a =\angle c = 45\°$