Bonus: in triangle stp, the measure of < t is twice the measure of < s and the
measure of < p is three times the measure of < s. what is the measure of all three angles?

enter only numbers in the boxes:
m< s = degrees

m< t= degrees

m< p= degrees

m∠S=30°

m∠T=60°

m∠P=90°

Step-by-step explanation:

we know that

The sum of the interior angles in a triangle must be equal to 180 degrees

so

In the triangle STP

m∠S+m∠T+m∠P=180° > equation A

m∠T=2(m∠S) > equation B

m∠P=3(m∠S) > equation C

Solve the system of equations by substitution

Substitute equation B and equation C in equation A

m∠S+2(m∠S)+3(m∠S)=180°

Solve for m∠S

6m∠S=180°

m∠S=30°

Find m∠T

m∠T=2(m∠S)

m∠T=2(30°)=60°

Find m∠P

m∠P=3(m∠S)

m∠P=3(30°)=90°

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)

answer: no

step-by-step explanation: because the big angle will spread away the 2 side that it is on and make the opposite side even longer.