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Find the value of x in each triangle. Give your reasons.
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6 partsStep-by-step solution
20 stepsHere are the values of for each triangle:
Part a· 2 steps
Identify the type of triangle.
The markings on two sides indicate that it is an isosceles triangle.
In an isosceles triangle, the angles opposite the equal sides are equal.
The angle is opposite one of the equal sides, and is opposite the other equal side.
Reason: Base angles of an isosceles triangle are equal.
The value of is .
Part b
Identify the type of triangle.
The markings on two sides indicate that it is an isosceles triangle.
In an isosceles triangle, the angles opposite the equal sides are equal.
The angle is one of the base angles, and is the other base angle.
Reason: Base angles of an isosceles triangle are equal.
The value of is .
Part c
Identify the type of triangle.
The markings on two sides indicate that it is an isosceles triangle.
In an isosceles triangle, the base angles (angles opposite the equal sides) are equal.
Let the base angles be . The vertex angle is .
The sum of angles in a triangle is .
The angle is one of the base angles.
Reason: Base angles of an isosceles triangle are equal, and the sum of angles in a triangle is .
The value of is .
Part d
Identify the type of triangle.
The markings on two sides indicate that it is an isosceles triangle.
In an isosceles triangle, the base angles (angles opposite the equal sides) are equal.
Let the base angles be . The vertex angle is .
The sum of angles in a triangle is .
The angle is one of the base angles.
Reason: Base angles of an isosceles triangle are equal, and the sum of angles in a triangle is .
The value of is .
Part e
Identify the type of triangle.
The markings on two sides indicate that it is an isosceles triangle.
In an isosceles triangle, the base angles (angles opposite the equal sides) are equal.
Let the base angles be . The vertex angle is .
The sum of angles in a triangle is .
The angle is one of the base angles.
Reason: Base angles of an isosceles triangle are equal, and the sum of angles in a triangle is .
The value of is .
Part f
Identify the type of triangle.
The markings on two sides indicate that it is an isosceles triangle.
The angle is an exterior angle.
The interior angle adjacent to it forms a linear pair.
This interior angle () is one of the base angles of the isosceles triangle.
Since the base angles are equal, the other base angle is also .
The sum of angles in a triangle is .
The angle is the vertex angle.
Reason: Angles on a straight line sum to , base angles of an isosceles triangle are equal, and the sum of angles in a triangle is .
The value of is .
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