Question

question 7 of 8 (1 point) | question attempt: 1 of 3
suppose that △ijk is isosceles with base \\(\overline{ik}\\).
suppose also that \\(m \angle i = (5x + 14)^circ\\) and \\(m \angle k = (3x + 30)^circ\\).
find the degree measure of each angle in the triangle.
\\(m \angle i = \square ^\circ\\)
\\(m \angle j = \square ^\circ\\)
\\(m \angle k = \square ^\circ\\)

Explanation:

Step1: Identify equal angles in isosceles triangle

In an isosceles triangle with base \( \overline{IK} \), the legs are \( \overline{IJ} \) and \( \overline{KJ} \), so the base angles \( \angle I \) and \( \angle K \) are equal. Thus, set \( 5x + 14 = 3x + 30 \).

Step2: Solve for \( x \)

Subtract \( 3x \) from both sides: \( 2x + 14 = 30 \). Subtract 14: \( 2x = 16 \). Divide by 2: \( x = 8 \).

Step3: Find \( m\angle I \) and \( m\angle K \)

Substitute \( x = 8 \) into \( m\angle I = 5x + 14 \): \( 5(8) + 14 = 40 + 14 = 54^\circ \). Same for \( m\angle K = 3(8) + 30 = 24 + 30 = 54^\circ \).

Step4: Find \( m\angle J \)

Sum of angles in a triangle is \( 180^\circ \). So \( m\angle J = 180 - 54 - 54 = 72^\circ \).

Answer:

\( m\angle I = 54^\circ \), \( m\angle J = 72^\circ \), \( m\angle K = 54^\circ \)