Question

sum of two angle of a triangle is 90 and their difference is 50. find all the angles of the triangle.

Answer 1

Since the sum of all angles in a triangle is 180 degrees.
So if the sum of two angles are 90 degrees.
Then the third angle=180-90=90 degrees.
The difference between the two angles are 50 degrees.
Then the first angle=70
As let first angle and second angle=x and y
Then x+y=90
x-y=50
2x=140
So. x=70
Since x+y=90
70+y=90
So. y=90-70=20 degrees.
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Answer 2

Given

Sum of two angles is 90

difference is 50

To find

measures of all angles of triangle

Solution

Let the angles be x & y

By the condition given in your question we get equation

x + y = 90. ... ( l )

x - y. = 50. ... ( ll )

adding equation ( l ) & ( ll ) we get

2x = 140

x = 70

putting x = 70 in equation ( l )

70 + y = 90

y = 90 - 70

y = 20

we know that

Sum of measures of all angles of triangle is 180

Let the third angle be a

so

70 + 20 + a = 180

90 + a = 180

a = 180 - 90

a = 90

so the measure of all angles of triangle are 20 , 70 & 90