Question

a quadrilateral has two angles that measure 60° and 195°. The other two angles are in a ratio of 5:16. What are the measures of those two angles?

Answer 1

Step-by-step explanation:

Given:-

A quadrilateral has two angles that measure 60° and 195°. The other two angles are in a ratio of 5:16.

To find:-

What are the measures of those two angles?

Solution:-

Given that

The measurements of the two angles of a quadrilateral = 60° and 195°

The ratio of other two angles of the quadrilateral = 5:16

Let they be 5X° and 16X°

We know that

The sum of all angles in the quadrilateral is 360°

=> 60°+195°+5X°+16X° = 360°

=> 255°+21X° = 360°

=>21X°=360°-255°

=>21X° = 105°

=> X° = 105°/21

=>X°=5°

The value of X=5°

Now,

5X°=5×5°=25°

16X°=16×5°=80°

Answer:-

The measurements of the other two angles of the given quadrilateral are 25° and 80°

Used formulae:-

The sum of all angles in the quadrilateral is 360°

Answer 2

Answer:

25, 80

Step-by-step explanation:

Let the two unknown angles be 5x and 16x.

Now,

195+60+5x+16x=360(Sum of all angles of quadrilateral)

or, 255+5x+16x=360

or, 21x=360-255

or, 21x=105

or, x=105/21

or, x=5

Therefore, 5x=5*5=25, 16x=16*5=80.