What is the measure of angle R?

52.5

Step-by-step explanation:

Since this is an isosceles triangle, the base angles are the same

The three angles add to 180

R+            T +              S = 180

3x+30   + 3x+30 + 12x-15 = 180

Combine like terms

18x +45 = 180

Subtract 45 from each side

18x+45 - 45 = 180-45

18x =135

Divide each side by 18

18x/18 = 135/18

x = 7.5

We want angle R

R = 3x+30

  = 3( 7.5) +30

  22.5 +30

   52.5

answer

d. 10

explanation

the distance from point y to wx is the height of the triangle.

using pythagoras theorem,

group similar terms to get,

this implies that,

take positive square root of both sides to get,

this implies that,

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).