Question

1. if (mangle def=(7x + 4)^{circ}), (mangle deg=(5x + 1)^{circ}), and (mangle gef = 23^{circ}), find each measure.

7x + 4 = 5x+1 + 23
x=
(mangle deg=)
(mangle def=)

Explanation:

Step1: Set up angle sum equation

$(5x + 1) + 23 = 7x + 4$

Step2: Simplify left side

$5x + 24 = 7x + 4$

Step3: Subtract 5x from both sides

$24 = 2x + 4$

Step4: Subtract 4 from both sides

$20 = 2x$

Step5: Solve for x

$x = 10$

Step6: Calculate m∠DEG

$5x + 1 = 5(10) + 1 = 51$

Step7: Calculate m∠DEF

$7x + 4 = 7(10) + 4 = 74$

Answer:

x = 10, m∠DEG = 51°, m∠DEF = 74°