Question

question 7: one angle in a triangle has a measure that is three times as large as the smallest angle. the measure of the third angle is 30 degrees more than that of the smallest angle. find the measure of the largest angle. answer: the largest angle has a measure of degrees. 0/3 pts 99 details
question 8: if chance has 2 times as many dimes as nickels and they have a combined value of 100 cents, how many of each coin does he have? 0/3 pts 99 details

Explanation:

Question 7

Step1: Let the smallest angle be $x$.

The largest angle is $3x$ and the third - angle is $x + 30$.

Step2: Use the angle - sum property of a triangle.

The sum of angles in a triangle is $180^{\circ}$, so $x+3x+(x + 30)=180$.

Step3: Combine like terms.

$5x+30 = 180$.

Step4: Subtract 30 from both sides.

$5x=180 - 30=150$.

Step5: Solve for $x$.

$x=\frac{150}{5}=30$.
The largest angle is $3x$. Substitute $x = 30$ into $3x$, we get $3\times30 = 90$.

Step1: Let the number of nickels be $x$.

Then the number of dimes is $2x$.

Step2: Set up an equation based on the value of the coins.

A nickel is worth 5 cents and a dime is worth 10 cents, and the total value is 100 cents. So $5x+10\times(2x)=100$.

Step3: Simplify the left - hand side of the equation.

$5x + 20x=100$, which gives $25x=100$.

Step4: Solve for $x$.

$x=\frac{100}{25}=4$.
The number of nickels is $x = 4$, and the number of dimes is $2x=8$.

Answer:

$90$

Question 8