Question

4 - 2 angles of triangles practice
find the measure of each of the numbered angles. then put them in order from greatest to least.
∠1
∠2
∠3
∠4
∠5
∠6

Explanation:

Step1: Find \( \angle1 \)

Use the exterior - angle theorem for the first triangle. The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles.
\( \angle1=36^{\circ}+68^{\circ}=104^{\circ} \)

Step2: Find \( \angle2 \)

Use the triangle - angle sum theorem (\( 180^{\circ} \) in a triangle). Let the triangle with \( \angle2 \) have angles \( \angle2\), \(36^{\circ}\), and \(68^{\circ}\).
\( \angle2 = 180^{\circ}-(36^{\circ}+68^{\circ})=180^{\circ}-104^{\circ}=76^{\circ} \)

Step3: Find \( \angle3 \)

Use the linear - pair relationship (sum to \( 180^{\circ} \)).
\( \angle3=180^{\circ}-(36^{\circ}+68^{\circ}) = 76^{\circ}\) (also, vertical angles with \( \angle2\))

Step4: Find \( \angle4 \)

Use the triangle - angle sum theorem for the triangle with \(82^{\circ}\), \(65^{\circ}\), and \( \angle4\).
\( \angle4=180^{\circ}-(82^{\circ}+65^{\circ})=180^{\circ}-147^{\circ}=33^{\circ} \)

Step5: Find \( \angle5 \)

Use the triangle - angle sum theorem for the triangle with \( \angle5\), \(70^{\circ}\), and \( \angle4\).
\( \angle5=180^{\circ}-(70^{\circ}+33^{\circ})=180^{\circ}-103^{\circ}=77^{\circ} \)

Step6: Find \( \angle6 \)

Use the linear - pair relationship (sum to \( 180^{\circ} \)).
\( \angle6=180^{\circ}-118^{\circ}=62^{\circ} \)

Answer:

\( \angle1 = 104^{\circ}\), \( \angle2 = 76^{\circ}\), \( \angle3 = 76^{\circ}\), \( \angle4 = 33^{\circ}\), \( \angle5 = 77^{\circ}\), \( \angle6 = 62^{\circ}\)
Order from greatest to least: \( \angle1(104^{\circ})>\angle5(77^{\circ})>\angle2(76^{\circ})=\angle3(76^{\circ})>\angle6(62^{\circ})>\angle4(33^{\circ}) \)