Question

Question 8 of 10What is the measure of ABC in the figure below?15459B15сO A. 15°B. 30°C. 45°D. 90°E. 15°F Cannot be determined

Answer 1

The measure of angle ABC is;

`90^(\circ)`

Step-by-step explanation:

Given the figure in the attached image.

`\begin{gathered} AB=CD \\ BC=AD \\ \text{ since} \\ AB=BC=15 \\ So; \\ AB=BC=CD=AD \end{gathered}`

Also;

Triangle BCD is an isosceles triangle;

`\begin{gathered} 2*\measuredangle\text{CBD}+90=180 \\ \measuredangle\text{CBD}=(90)/(2)=45^(\circ) \end{gathered}`

Then we have;

`\begin{gathered} m\measuredangle ABC=m\measuredangle ABD+m\measuredangle CBD \\ m\measuredangle ABC=45^(\circ)+45^{\circ^{}} \\ m\measuredangle ABC=90^(\circ) \end{gathered}`

Therefore, the measure of angle ABC is;

`90^(\circ)`