What is the measure of y? (hint- find the sum of the interior angles first)if the angles are 112° and 88° and 135° what is the measure of y? a.115b.540c.205

Option A 115.

Step-by-step explanation:

In any quadrilateral having number of sides = n

Sum of all interior angles is = ( n-2 ) × 180°

Now in this question number of sides are n = 5

so sum of interior angles = (5 - 2) × 180°

                                          = 3 × 180°

                                          = 540°

Now sum of all interior angles = 90 + 135 + y + 88 + 112

                                                  = 425 + y

By the definition of interior angles.

425 + y = 540

          y = 540 - 425

              = 115°

Therefore, option A is the answer.

m∠a is 90°

m∠b is 40°

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west