In ∆ABC the angle bisectors drawn from vertices A and B intersect at point D. Find m∠ADB if: m∠C=γ
1 answer:
Answer:
∠ADB = γ/2 +90°
Step-by-step explanation:
Here's one way to show the measure of ∠ADB.
∠ADB = 180° - (α + β) . . . . . sum of angles in ΔABD
∠ADB + (2α +β) + γ + (2β +α) = 360° . . . . . sum of angles in DXCY
Substituting for (α + β) in the second equation, we get ...
∠ADB + 3(180° - ∠ADB) + γ = 360°
180° + γ = 2(∠ADB) . . . . . . add 2(∠ADB)-360°
∠ADB = γ/2 + 90° . . . . . . . divide by 2
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To find angles CXD and CYD, we observe that these are exterior angles to triangles AXB and AYB, respectively. As such, those angles are equal to the sum of the remote interior angles, taking into account that AY and BX are angle bisectors.
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Step-by-step explanation:
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Answer:
and
Step-by-step explanation:
We must solve the quadratic equation to find the values of x that satisfy equality
Subtract 24 on both sides of equality
Now we factor the quadratic equation
Identify two numbers that when you add them you get as a result 2 and when you multiply them you get as a result -24
The numbers sought are: 6 and -4
So the factors are:
Finally note that the solutions are:
and
