Question

δijk ~ δuts. what are m∠j and m∠i?

m∠j = \boxed{\space}°
m∠i = \space °

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle IJK\sim\triangle UTS\), corresponding angles are equal.

Step2: Find \(m\angle J\)

In \(\triangle UTS\), using the angle - sum property of a triangle (\(180^{\circ}\) in a triangle). Let \(m\angle S = x\). Then \(60^{\circ}+60^{\circ}+x = 180^{\circ}\), so \(x = 60^{\circ}\). \(\angle J\) corresponds to \(\angle S\). So \(m\angle J=60^{\circ}\)

Step3: Find \(m\angle I\)

\(\angle I\) corresponds to \(\angle U\). So \(m\angle I = 60^{\circ}\)

Answer:

\(m\angle J = 60^{\circ}\)
\(m\angle I=60^{\circ}\)