a quadrilateral has two angles that measure 88 and 62. the other two angles are in a ratio of 16:19. what are the measures of those two angles?

let the remaining two angles be 16x and 19x

16x+19x+88+62 = 360

ok, up to you...

To find the measures of the other two angles in the quadrilateral, we can follow these steps:

Step 1: Determine the sum of all angles in a quadrilateral. In a quadrilateral, the sum of all the angles is always 360 degrees.

Step 2: Find the sum of the given angles. We are given that two angles measure 88 degrees and 62 degrees, so their sum is 88 + 62 = 150 degrees.

Step 3: Subtract the sum of the given angles from the total sum of angles in a quadrilateral. 360 - 150 = 210 degrees.

Step 4: Convert the ratio of the other two angles into a fraction. The ratio given is 16:19, so the fraction becomes 16/19.

Step 5: Set up an equation using the fraction. Let x be the measure of the smaller angle, then the larger angle can be represented as (16/19)x.

Step 6: Set up another equation using the formula for the sum of the two angles. Since the two angles are in a ratio of 16:19, the equation becomes x + (16/19)x = 210.

Step 7: Solve the equation to find the value of x. Multiply through by 19 to remove the fraction: 19x + 16x = 3990. Combine like terms: 35x = 3990. Solve for x: x = 3990/35 = 114.

Step 8: Find the measure of the larger angle. Substitute the value of x into the equation (16/19)x to get (16/19)*114 = 96.

Therefore, the measures of the other two angles in the quadrilateral are 114 degrees and 96 degrees.