Question

If angle CED is 35 degrees and ADC is 50 degrees, what is the measure of angle DCE?

Answer 1

Step-by-step explanation:

The diagram for this problem is shown below. We know some facts:

`\angle CED=35^(\circ) \\ \\ \angle ADC=50^(\circ)`

From the figure,
`\angle ADE=180^(\circ)`, so we can write this relationship:

`\angle ADC+\angle CDE=180^(\circ) \\ \\ \\ Isolating \ \angle CDE: \\ \\ \angle CDE=180^(\circ)-\angle ADC \\ \\ \\ Substituting \ angle ADC=50^(\circ) \\ \\ \angle CDE=180^(\circ)-50^(\circ) \\ \\ \angle CDE=130^(\circ)`

Since C, E and D form a triangle, then the internal angles of any triangle add up to 180 degrees, so:

`\angle CED + \angle EDC + \angle DCE=180^(\circ) \\ \\ \\ Substituting \ know \ values: \\ \\ 35^(\circ)+ 130^(\circ)+ \angle DCE=180^(\circ) \\ \\ \\ Isolating \ \angle DCE: \\ \\ \angle DCE=180^(\circ) -35^(\circ)-130^(\circ) \\ \\ \boxed{\angle DCE=15^(\circ)}`