Question

independent practice
write and solve an equation to find the measures of each angle in the triangles

triangle	equation and work	angle measures
2. triangle with vertices d, e, f. angle at d: (x + 20)°, angle at e: (3x)°, angle at f: 36°	(with a handwritten \=180\)	∠d = 51, ∠e = 93, ∠f = 36
3. triangle with vertices g, h, i. angle at g: 28°, sides gh and gi are marked (isosceles?); angle at h: x°	(with a handwritten \=180\)	∠g =, ∠h =, ∠i =
4. triangle with vertices j, k, l. angle at j: 41°, angle at k: (5x - 5)°, angle at l: (3x)°	(with a handwritten \=180\)	∠j =, ∠k =, ∠l =

(and a partial line about \angle pairs form complementary\)

Explanation:

Problem 1:

Step1: Sum of angles in a triangle is \(180^\circ\). So, \(63 + (2x + 8) + (x + 7) = 180\).

Step2: Simplify the left side: \(63 + 2x + 8 + x + 7 = 3x + 78\). So, \(3x + 78 = 180\).

Step3: Subtract 78 from both sides: \(3x = 180 - 78 = 102\).

Step4: Divide by 3: \(x = \frac{102}{3} = 34\).

Step5: Find each angle: \(\angle A = 2(34) + 8 = 76^\circ\), \(\angle B = 63^\circ\), \(\angle C = 34 + 7 = 41^\circ\).

Step1: Sum of angles in a triangle is \(180^\circ\). So, \((x + 20) + 3x + 36 = 180\).

Step2: Simplify the left side: \(4x + 56 = 180\).

Step3: Subtract 56: \(4x = 180 - 56 = 124\).

Step4: Divide by 4: \(x = 31\).

Step5: Find each angle: \(\angle D = 31 + 20 = 51^\circ\), \(\angle E = 3(31) = 93^\circ\), \(\angle F = 36^\circ\).

Step1: The triangle is isosceles (two sides marked equal), so \(\angle H = \angle I = x\). Sum of angles: \(28 + x + x = 180\).

Step2: Simplify: \(28 + 2x = 180\).

Step3: Subtract 28: \(2x = 180 - 28 = 152\).

Step4: Divide by 2: \(x = 76\). So, \(\angle G = 28^\circ\), \(\angle H = 76^\circ\), \(\angle I = 76^\circ\).

Answer:

\(\angle A = 76^\circ\), \(\angle B = 63^\circ\), \(\angle C = 41^\circ\)

Problem 2: