Question

what is the value of z?
(there is a geometric figure with points s, t, u, v. angles and expressions: 6z, z+60, 41°, 41°, right angles at v and t.)
z =
submit

Explanation:

Step1: Use the Hypotenuse - Leg (HL) Congruence Theorem

Since the two right - angled triangles have a common hypotenuse and one pair of equal angles ($41^{\circ}=41^{\circ}$), they are congruent. So, $6z=z + 60$.

Step2: Solve the equation for $z$

Subtract $z$ from both sides: $6z−z=z + 60−z$.
This gives $5z=60$.
Divide both sides by $5$: $z=\frac{60}{5}$.

Answer:

$12$