Question

What is the measure of angle c?

Answer 1

59 degrees

Explanation:

Since ABCD is a cyclic quadrilateral,

then

`angle ABC + angle ADC = 180`
(opposite angles in cyclic quadrilateral are equal to 180 degrees)

`2x+3+4x+3=180`
`6x+6=180`
`6x=174`
`x=29`

Since `angle BCD = 2x+1`, then you just sub in `x=29`

ie. `angle BCD = 2(29)+1 = 59`

Answer 2

`color(blue)(59^@)`

Explanation:

Opposite angles in a cyclic quadrilateral are supplementary.

So:

`/_B+/_D=180^@`

`/_B+/_D=(2x+3)+(4x+3)=180^@`

`\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \=6x+6=180`

`x=(180-6)/6=29^@`

`/_C=2x+1=2(29)+1=59^@`

Answer 3

Measure of `color(indigo )(hat C = 59^@`

Explanation:

Given `hatB = 2x + 3, hat C = 2x + 1, hat D = 4x + 3`

To find measure of `hat C`

It’s a cyclic quadrilateral and hence sum of opposite angles equals `180^@`

i. e. `hat A + hat C = hat B + hat D = pi^c = 180^@`

`hat B + hat D = 2x + 3 + 4x + 3 = 180^@`

`6x + 6 = 180`

`x = (180 - 6) / 6 = 29^@`

`hat C = 2x + 1 = (2*29 + 1) = 59^@`