Question

Given ∠ABD = 70°, ∠CBD = 5x + 13°, ∠ABC = 3x + 33°, find ∠ABC.

a) 23°
b) 33°
c) 43°
d) 53°

Answer 1

To find ∠ABC, we can use the fact that the sum of the angles in a triangle is 180°. Given the values of ∠ABD and ∠CBD, we can set up an equation and solve for x to find ∠ABC.

Step-by-step explanation:

To find ∠ABC, we can use the fact that the sum of the angles in a triangle is 180°. Given that ∠ABD = 70°, ∠CBD = 5x + 13°, and ∠ABC = 3x + 33°, we can set up an equation:

∠ABD + ∠CBD + ∠ABC = 180°

Substituting the given values:

70° + (5x + 13°) + (3x + 33°) = 180°

Simplifying:

8x + 116° = 180°

Subtracting 116° from both sides:

8x = 64°

Dividing both sides by 8:

x = 8°

Now we can find ∠ABC by substituting x in the equation:

∠ABC = 3(8°) + 33° = 24° + 33° = 57°