Final answer:
The remaining two angles of the quadrilateral are 15° and 95°, found by subtracting the given angles from 360° and dividing the result in a 3:19 ratio.
Step-by-step explanation:
To find the measures of the two angles in the given ratio, we can use the fact that the sum of all angles in a quadrilateral is 360°.
Let’s denote the measures of the two unknown angles as 3x and 19x, where x is a common multiplier.
We know that the sum of all angles in a quadrilateral is 360°.
Therefore, we can set up an equation based on this fact:
155° + 95° + 3x + 19x = 360°
Combining like terms, we get:
250° + 22x = 360°
Subtracting 250° from both sides gives us:
22x = 110°
Dividing both sides by 22 yields:
x = 5°
Now that we have found the value of x, we can find the measures of the two unknown angles:
3x = 3 × 5° = 15°
19x = 19 × 5° = 95°
Therefore, the measures of the two angles in the ratio of 3:19 are 15° and 95°.