To be able to answer the questions, let us first solve for the value of x.
☞Notice that the angle with a measure of 3x+18 and the angle with an measure of 5x–14 are supplementary. Thus,
12. What is m∠1?
SOLUTION:
∠1 and the angle with a measure of 5x–14 are alternate exterior angles (angles that lie outside the parallel lines and on the opposite sides of the transversal) hence, they are congruent.
2. What is m∠3?
SOLUTION:
∠3 and the angle with a measure of 3x+18 are vertical angles (non-adjacent angles that are formed when lines intersect) hence, they are congruent.
3. What is m∠2
SOLUTION:
∠2 and the angle with a measure of 5x–14 are corresponding angles (angles that relatively have the same position that lie on the same side of the transversal) hence, they are congruent.
4. What is m∠4?
∠4 and the angle with a measure of 5x–14 form a linear pair (a pair of adjacent and supplementary angles) hence, the sum of their measures is 180°
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Verified answer
To be able to answer the questions, let us first solve for the value of x.
☞Notice that the angle with a measure of 3x+18 and the angle with an measure of 5x–14 are supplementary. Thus,
12. What is m∠1?
SOLUTION:
∠1 and the angle with a measure of 5x–14 are alternate exterior angles (angles that lie outside the parallel lines and on the opposite sides of the transversal) hence, they are congruent.
2. What is m∠3?
SOLUTION:
∠3 and the angle with a measure of 3x+18 are vertical angles (non-adjacent angles that are formed when lines intersect) hence, they are congruent.
3. What is m∠2
SOLUTION:
∠2 and the angle with a measure of 5x–14 are corresponding angles (angles that relatively have the same position that lie on the same side of the transversal) hence, they are congruent.
4. What is m∠4?
∠4 and the angle with a measure of 5x–14 form a linear pair (a pair of adjacent and supplementary angles) hence, the sum of their measures is 180°