Question

Angles of the triangle are in AP.If the smallest angle is45°.Find the largest angle.​

Answer 1

Solution

so the series is ..

(45°),(45°+d),(45°+2d)

where D is the difference

now..

45°+(45°+d)+(45°+2d)=180°

=>3d=180°-135°

=>d=45°/3=15°

therefore the largest angle is

=45°+2(15°)=75°

hope this helps you.......

Answer 2

Answer:

As given that angles of a triangle are in AP.

Given that first

term of AP is 45° as the smallest angle is 45°.

Now let us assume that common difference of the AP is x.

So three terms will be:-)

45,45+x,45+2x.

also we know that sum of all all angles in a triangle is 180°.

So,

$45 +( 45 + x) + (45 + 2x) = 180 \\ \implies135 + 3x = 180 \\ \implies3x = 45 \\ \implies \: x = \frac{45}{3} = 15$

So the angles will be:-

So the angles will be:-45,45+15,45+30

So the angles will be:-45,45+15,45+30=45°,60°,75°.

By this we get that largest angle is

75°