Question

85. Use the given figure to find the angle x. ​

Answer 1

Answer:

x = 36°.

Step-by-step explanation:

In the diagram Shown below.

If two sides are equal then the angles opposite to the same two sides are also equal.

Consider triangle CAB

∠CAB = ∠CBA = 36°.

Sum of two interior angles is equal to exterior angle.

∠BCD=∠CAB + ∠CBA

Plug values.

∠BCD=36°+36°

Simplify.

∠BCD=72°

Now consider triangle BCD.

If two sides are equal then the angles opposite to the same two sides are also equal.

∠BCD=∠BDC = 72°

Sum of the all angles in a triangle is equal to 180°.

∠BCD+∠BDC+∠CBD = 180°

Plug all values.

72°+72°+x = 180°

Isolate x.

x = 180°-144°

x = 36°.