The measures of two complementary angles are in the ratio 8:1. how many degrees are in the larger angle?

1 answer:

4 0

Since the measures of the two angles are in the ratio 8:1, this means the bigger angle's is 8x and the smaller angle is x. Since they are complementary, they add to 90°, so you create the equation 8x+x=90°. This can be simplified to 9x=90°. Then, you divide 90 by 9 to get 10. This means x=10. Next, you replace x with 10 to find the measure of the bigger angle. 8x10=80, so the larger angle is 80°.

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A mother has two children whose ages differ by 5 years. The sum of the squares of their ages is 97. The square of the mother's

svetoff [14.1K]

Answer:

41 years old.

Step-by-step explanation:

Let x represent age of younger child.

We have been given that a mother has two children whose ages differ by 5 years. So the age of older child would be $x+5$ .

The sum of the squares of their ages is 97. We can represent this information in an equation as:

$x^2+(x+5)^2=97$

Let us solve for x.

$x^2+x^2+10x+25=97$

$2x^2+10x+25-97=0$

$2x^2+10x-72=0$

Divide both sides by 2:

$x^2+5x-36=0$

$x^2+9x-4x-36=0$

$x(x+9)-4(x+9)=0$

$(x+9)(x-4)=0$

$(x+9)=0 ; (x-4)=0$

$x=-9 ; x=4$

Since age cannot be negative, therefore, age of younger child is 4 years.

Age of older child would be $x+5\Rightarrow4+5=9$

Therefore, the age of older child would be 9 years.

We have been given that the square of the mother's age can be found by writing the squares of the children's ages one after the other as a four-digit number.

Square of 4: $4^2=16$