Question

Suppose we have isosceles triangle BCD and isosceles triangle ACD
How can we solve for angle ∠BAD?
∠ABD is 18
∠ADC is 32

answer correctly for brainliest

Answer 1

Answer:

∠BAD = 122°

Step-by-step explanation:

You have overlapping isosceles triangles with half the a.pex angle of the taller being 18° and the base angle of the shorter being 32°. You want to know the measure of the obtuse central angle.

Angle relations

There are several angle relations that could come into play in this figure. The one that seems easiest to use is the congruence of alternate interior angles.

Application

Drawing segment AE parallel to base CD divides angle BAD into two parts. One of them is right angle BAE, and the other is acute angle EAD. That acute angle is an alternate interior angle with respect to transversal AD and parallel segments AE and DC. Hence ...

  ∠EAD = ∠ADC = 32°

  ∠BAD = ∠BAE +∠EAD = 90° +32°

  ∠BAD = 122°

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Additional comment

The measure of angle ABD is irrelevant, as long as it is less than 58°.