Area = base * height = 8 * 5 = 40 cm²

Opposite side = hypotenuse * sin(30°) = 10 * 1/2 = 5 cm.

The sum of the angles in a triangle is always 180 degrees. Therefore, if two angles are 45 degrees each, the third angle = 180 - (45 + 45) = 90 degrees.

The sum of angles in a triangle is 180 degrees. Therefore, the third angle = 180 - (50 + 60) = 70 degrees.

The sum of angles in a triangle is 180 degrees. Therefore, the third angle = 180 - 60 - 80 = 40 degrees.

The maximum length of the third side = sum of the other two sides - 1 = 7 + 10 - 1 = 16 cm.

The sum of angles in a triangle is 180 degrees. Therefore, angle C = 180 - (30 + 60) = 90 degrees.

Since two angles are equal (45 degrees), triangle DEF is an isosceles triangle.

Since two angles are equal (45 degrees), triangle DEF is an isosceles triangle.

Using the Pythagorean theorem, 5^2 + 12^2 = 25 + 144 = 169 = 13^2. Thus, triangle DEF is a right triangle.

Using the sine rule, HI/sin(60) = GH/sin(30). Therefore, HI = (10 * sin(60)) / sin(30) = 10 * (√3/2) / (1/2) = 10√3 cm.

The longest side of triangle GHI is GI, which measures 26 cm.

Semi-perimeter = (JK + KL + JL) / 2 = (15 + 20 + 25) / 2 = 30 cm.

Semi-perimeter = (JK + KL + JL) / 2 = (15 + 20 + 25) / 2 = 30 cm.

Perimeter = PQ + QR + PR = 8 + 6 + 10 = 24 cm.

Semi-perimeter = (PQ + QR + PR) / 2 = (8 + 6 + 10) / 2 = 12 cm.

In an isosceles right triangle, the sides opposite the 45-degree angles are equal. Therefore, XY = XZ / √2 = 10 / √2 = 5√2 cm.

In an isosceles triangle with angles 45 degrees, the sides opposite these angles are equal, hence the ratio is 1:1.

Circumference = 2πr => r = circumference / (2π) = 31.4 / (2 * 3.14) = 5 cm

Using Heron's formula, s = (5 + 12 + 13)/2 = 15. Area = √[s(s-a)(s-b)(s-c)] = √[15(15-5)(15-12)(15-13)] = √[15*10*3*2] = √[900] = 30 cm².

Using the Pythagorean theorem, 7^2 + 24^2 = 49 + 576 = 625 = 25^2. Therefore, triangle ABC is a right triangle.

This is a right triangle. Area = 1/2 * base * height = 1/2 * 5 * 12 = 30 cm².

The distance between the centers of two externally tangent circles is the sum of their radii: 3 + 4 = 7 cm.

Distance between centers = r1 + r2 = 3 cm + 5 cm = 8 cm.

The distance between the centers of two externally tangent circles is the sum of their radii: 3 + 4 = 7 cm.

If two lines are perpendicular, the sum of their angles is 90 degrees. Therefore, if one line makes an angle of 30 degrees with the horizontal, the other line must make an angle of 90 - 30 = 60 degrees with the horizontal.

Perpendicular lines intersect at right angles, which measure 90 degrees.

Adjacent angles formed by intersecting lines are supplementary. Therefore, 180 - 70 = 110 degrees.

Alternate interior angles are equal when two parallel lines are cut by a transversal. Therefore, if one angle is 65 degrees, the other alternate interior angle is also 65 degrees.

Area = πr² = 3.14 * (4)² = 3.14 * 16 = 50.24 cm²