Question

How do I find each measure? Please I need answers ASAP it's due at 1:50

Answer 1

Angle CAD is 44 degrees

Angle ACD is 44 degrees

Angle ACB is 136 degrees

Angle ABC is 22 degrees

Step-by-step explanation:

29. Triangle ADC is an isosceles triangle because it has two equal sides.

If segments AD and DC are congruent, then segment AC is the base and the base angles of an isosceles triangle are equal.

Let x be angle CAD.

Let's go ahead x;

`\begin{gathered} 92+x+x=180\text{ (sum of angles in a triangle)} \\ 92+2x=180 \\ 2x=180-92 \\ 2x=88 \\ x=(88)/(2) \\ \therefore x=44^(\circ) \end{gathered}`

Therefore, measure of angle CAD is 44 degrees.

30. Measure of angle ACD is 44 degrees (Base angles of an isosceles triangle are equal)

31. Let angle ACB be y,

Let's go ahead and find measure of angle ACB;

`\begin{gathered} 44+y=180\text{ (angles on a straight line)} \\ y=180-44 \\ \therefore y=136^(\circ) \end{gathered}`

So measure of angle ACB is 136 degrees.

32. Let angle ABC be z.

Triangle ACB is also an isosceles triangle so the base angles are the same.

Let's go ahead and find z;

`\begin{gathered} 136+z+z=180_{}\text{ (sum of angles in a triangle)} \\ 138+2z=180 \\ 2z=180-136 \\ 2z=44 \\ z=(44)/(2) \\ \therefore z=22^(\circ) \end{gathered}`

So measure of angle ABC is 22 degrees.