Question

One of exterior angle of triangle is 105 degree and the interior opposite angles are in the ratio 2:5 find the angle of a tringle

Answer 1

TO FIND :-

Angles in a triangle whose exterior angle is 105° and interior opposite angles are in the ratio of 2:5

ANSWER :-

The angles in the triangle are 30°,75° and 75°

SOLUTION :-

Ratio = 2:5

Let the two angles be 2x and 5x

As we know that

Sum of two interior opposite angles = exterior angle

2x + 5x = 105

7x = 105

x = 105/7

x = 15°

Substituting x in 2x and 5x respectively

2x = 2(15) = 30°

5x = 5(15) = 75°

sum of angles in a triangle = 180°

30 + 75 + k = 180

105 + k = 180

k = 180 - 105

k = 75°

Answer 2

SEE THE ATTACHMENT FOR FIGURE.

SOLUTION:

ANGLE ACX=105°

AND AS WE KNOW

EXTERIOR ANGLE OF A TRIANGLE IS EQUAL TO THE SUM OF OPPOSITE ANGLES.

ANGLE ACX

=ANGLE ABC+ANGLE BAC

BUT IT IS GIVEN

ANGLE ABC/ANGLE BAC =2/5

SO

ANGLE ABC

=2/5 (ANGLE BAC)

HENCE

ANGLE ABC+ANGLE BAC =ANGLE ACX

ANGLE BAC

+(ANGLE BAC)2/5=105°

7(ANGLE BAC)/5=105°

ANGLE BAC=105°×5/7

ANGLE BAC=(15×5)°

ANGLE BAC =75°

ANGLE ABC=30°

ANGLE ACB=75°

thanks for asking