In triangle ABC, angle ABC = 50 degrees, D belongs to BC, angle BAD = 10 degrees
| March 8, 2021 | education
In triangle ABC, angle ABC = 50 degrees, D belongs to BC, angle BAD = 10 degrees, angle DAC = 60 degrees, AD = 7cm. Find the perimeter of triangle ADC.
In triangle ABD we calculate the value of the angle ADB.
Angle ADB = (180 – BAD – ABD) = (180 – 10 – 50) = 120.
Since the angles ADB and ADC are adjacent, the angle ADC = (180 – ADB) = (180 – 120) = 60.
In the ACD triangle, the angle ADC = CAD = 60, and therefore the angle ACD = (180 – 60 – 60) = 60, and then the ACD triangle is equilateral.
Then AC = CD = AD = 7 cm.
The perimeter of the triangle ADC will be equal to: Rads = (AC + CD + AD) = 3 * 7 = 21 cm.
Answer: The perimeter of the ACD triangle is 21 cm.
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