In the diagram shown, chords AB and CD intersect at E. The measure of (AC) ̂ is 134°, the measure of (DB) ̂ is (3x)° and the measure of ∠AEC is (7x)°. What is the degree measure of ∠ AED?

Question

contestada

Respuesta :

calculista calculista · Answer 1 · 2019-03-17T01:52:56+01:00

Answer:

The measure of angle AED is [tex]94\frac{8}{11}\°[/tex]

Step-by-step explanation:

step 1

Find the measure of x

we know that

The measure of the interior angle is the semi-sum of the arcs comprising it and its opposite

In this problem

m<AEC is a interior angle

so

[tex]m<AEC=\frac{1}{2}(arc\ AC+arc\ DB)[/tex]

substitute the values and solve for x

[tex]7x\°=\frac{1}{2}(134\°+3x\°)[/tex]

[tex]14x\°=(134\°+3x\°)[/tex]

[tex]14x\°-3x\°=134\°[/tex]

[tex]11x\°=134\°[/tex]

[tex]x=(134/11)\°[/tex]

step 2

Find the measure of angle AED

we know that

[tex]m<AEC+m<AED=180\°[/tex] -----> by supplementary angles

[tex]m<AED=180\°-m<AEC[/tex]

[tex]m<AED=180\°-7x[/tex]

[tex]m<AED=180\°-7(134/11)\°[/tex]

[tex]m<AED=180\°-(938/11)\°[/tex]

[tex]m<AED=(1,042/11)\°[/tex]

Convert to mixed number

[tex](1,042/11)\°=(1,034/11)\°+(8/11)\°=94\°+(8/11)\°=94\frac{8}{11}\°[/tex]