Question

$\triangle abd \cong \triangle cdb$. find x.
$\angle adb=(4x-35)^\circ$, $\angle cbd=(2x+17)^\circ$

Explanation:

Step1: Set congruent angles equal

Since $\triangle ABD \cong \triangle CDB$, corresponding angles $\angle ADB$ and $\angle CBD$ are equal:
$4x - 35 = 2x + 17$

Step2: Isolate x terms

Subtract $2x$ from both sides:
$4x - 2x - 35 = 17$
$2x - 35 = 17$

Step3: Solve for x

Add 35 to both sides, then divide by 2:
$2x = 17 + 35$
$2x = 52$
$x = \frac{52}{2}$

Answer:

$x = 26$