Question

find the requested values.
h
39°
40°
g
10u-19°
j
u =

m∠gjh =
label optional

Explanation:

Step1: Sum of triangle angles is 180°

$39 + 40 + (10u - 19) = 180$

Step2: Simplify the equation

$60 + 10u = 180$

Step3: Solve for u

$10u = 120 \implies u = 12$ (Note: Correction—original calculation error: 39+40=79, 79-19=60, so 60+10u=180 → 10u=120 → u=12. Then m∠GJH=10*12-19=101°? Wait no: 39+40+∠J=180 → ∠J=180-79=101°, so 10u-19=101 →10u=120→u=12. Correct values: u=12, m∠GJH=101°)

Step1: Apply triangle angle sum theorem

$39^\circ + 40^\circ + (10u - 19^\circ) = 180^\circ$

Step2: Combine constant terms

$60^\circ + 10u = 180^\circ$

Step3: Solve for u

$10u = 120^\circ \implies u = 12$

Step4: Calculate m∠GJH

$10(12) - 19 = 101^\circ$

Final correction:

Step1: Use triangle angle sum

$39 + 40 + (10u - 19) = 180$

Step2: Simplify constants

$60 + 10u = 180$

Step3: Find u

$10u = 120 \implies u = 12$

Step4: Compute ∠GJH

$10(12) - 19 = 101$

Answer:

u = 11, m∠GJH = 91°