Question

find the measure of x and y in the given triangle




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Answer 1

Answer:

x = 100°

y = 40°

Step-by-step explanation:

x is an exterior angle of ΔABC.

Given that, ∠BAC = 80° and it is linearly adjacent to x.

∴ x + ∠BAC = 180°

=> x + 80° = 180°

=> x = 180° - 80° = 100°

Also given that, the other exterior angle ∠ACX = 120°, which is the sum of distant interior angles ∠BAC and ∠ABC

∴ y + 80° = 120°

∴ y = 120° - 80° = 40°

Answer 2

Question

Find the measure of X and y in the given triangle

Concept used

Here the concept of exterior angle property and adjacent angle property is used..

✏️Adjacent angle property- the sum of adjacent angles is 180°

✏️Exterior angle property- The exterior angle theorem states that the measure of each exterior angle of a triangle is equal to the sum of the opposite and non-adjacent interior angles.

Solution

$\sf{80 \degree + y \degree = 120 \degree} [exterior \: angle \: property] \\ \sf{ y \degree = 120 - 80} \\ \sf{ y \degree =40 \degree }$

$\sf{ x \degree + 80 \degree = 180 \degree} [adjacent \: angl es] \\ \sf{x \degree = 180 - 80} \\ \sf{ x \degree = 100 \degree}$

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