Given:
AB
≅
BC
and AD = 10 in
m∠BDC = 90°
m∠ABC = 130°
Find: m∠ DBC, AC

A) and  

B) and  

Step-by-step explanation:

The picture of the question in the attached figure

Problem A

we know that

Triangle ABC has two equal sides

AB  ≅

BC

so

Is an isosceles triangle

therefore

Remember that

The altitude to the base of an isosceles triangle bisects the vertex angle. and bisects the base

In this problem segment BD represent the altitude to the base of an isosceles triangle ABC

so

Part 1) Find the measure of angle DBC

we have

substitute

Part 2) Find the value of segment AC

we have

substitute

Problem B

we know that

Triangle ABC has two equal sides

AB  ≅

BC

so

Is an isosceles triangle

therefore

Remember that

The altitude to the base of an isosceles triangle bisects the vertex angle. and bisects the base

In this problem segment BD represent the altitude to the base of an isosceles triangle ABC

so

Part 1) Find the measure of angle DBC

we have

substitute

Part 2) Find the value of segment AC

we have

substitute

answer: asdfghjkl,mnbv

step-by-step explanation: