What is the measure of angle a?

38°

Step-by-step explanation:

Using the Cosine rule in Δ ABC

cos A =

where a, b and c are the sides of the triangle.

Here a = 5, b = 3 and c = 7 , thus

cos A = = = , thus

∠ A = ( ) ≈ 38°

(2x + 16) + (x) = 180

step-by-step explanation:

given,

abcd is a quadrilateral inscribed in a circle

angle a is labeled x plus 16, (x + 16)

angle b is labeled x degrees, (x)

angle c is labeled 6x minus 4, (6x – 4)

angle d is labeled 2x plus 16, (2x + 16)

what equation can be used to solve for angle b?

we know that the sum of the opposite angles of a simple quadrilateral inscribed in a circle is 180 degrees.

angle b is opposite angle d

therefore, angle b + angle d = 180

(x) + (2x + 16) = 180 

same as (2x + 16) + (x) = 180