Question

to color the picture above

1. triangle with 65°, 65°, r
2. right triangle with 29°, right angle, r
3. r triangle with 72°, 38° 3x=78+...? x=26° (green)
4. r right triangle with 42°, right angle (orange)
5. r triangle with (2x)°, (x+24)°, (x)° (blue)
6. r triangle with (x+20)°, (6x)°, (3x)° (pink?)

Explanation:

Answer:

For problem 7 (triangle with angles \(72^\circ\), \(38^\circ\), and angle at \(R\)):
The sum of angles in a triangle is \(180^\circ\), so angle \(R = 180 - 72 - 38 = 70^\circ\) (assuming the handwritten "3x=78" was a miscalculation; correct calculation: \(72 + 38 = 110\), \(180 - 110 = 70\))

For problem 11 (triangle with angles \((2x)^\circ\), \((x + 24)^\circ\), \(x^\circ\)):
Sum of angles: \(2x + (x + 24) + x = 180\)
\(4x + 24 = 180\)
\(4x = 156\)
\(x = 39\)
Angles: \(2x = 78^\circ\), \(x + 24 = 63^\circ\), \(x = 39^\circ\)

For problem 12 (triangle with angles \((x + 20)^\circ\), \((6x)^\circ\), \((3x)^\circ\)):
Sum of angles: \((x + 20) + 6x + 3x = 180\)
\(10x + 20 = 180\)
\(10x = 160\)
\(x = 16\)
Angles: \(x + 20 = 36^\circ\), \(6x = 96^\circ\), \(3x = 48^\circ\)

(Note: For problem 3, if it's an isosceles triangle with two \(65^\circ\) angles, angle \(R = 180 - 65 - 65 = 50^\circ\) (matches the "50" handwritten). For problem 4 (right triangle with \(29^\circ\)), the other acute angle is \(90 - 29 = 61^\circ\). For problem 8 (right triangle with \(42^\circ\)), the other acute angle is \(90 - 42 = 48^\circ\).)