Answer: The larger measure be decreased by 8% so that the two angles remain complementary .
Step-by-step explanation:
Given : The ratio of measures of two complementary angles is 4 to 5.
Let the complementary angles are 4x and 5x ( indegrees) .
Since the sum of complementary angle is 90°.
Then, 4x+5x =90
9x=90
x= 10 [Divide both sides by 9]
Then , first angle = 4 (10)=40 °
Seconds angle = 5(10) = 50°
Smallest measure = 40°
The smallest measure is increased by 10%. , new angle = 40°+ 10% of 40°
= 40°+ (0.10)(40°)
= 40°+ 4°= 44°
Complement of 44° = 90°-44° = 46 °
Decrease in larger angle = 50°- 46° = 4°
Percent decrease in larger angle = [tex]\dfrac{\text{New angle}}{\text{Original angle}}\times100[/tex]
[tex]\dfrac{4}{50}\times100=8\%[/tex]
Hence, the larger measure be decreased by 8% so that the two angles remain complementary .
