Answer:
The measure of angle x is 68°
Step-by-step explanation:
The isosceles triangle has two sides equal, the angle between these two sides is called the vertex angle, the other two angles are called the base angles and they are equal in measures
In the given figure
∵ An isosceles Δ has a vertex angle of measure 68°
∴ The other two angles are equal in measure ⇒ base angles
→ The sum of the measures of the interior angles of a triangle is 180°
∴ The sum of the measures of the base angles = 180° - 68°
∴ The sum of the measures of the base angles = 112°
→ Divide their sum by 2 to find the measure of each angle
∵ The measure of each base angle = 112° ÷ 2
∴ The measure of each base angle = 56°
∵ There are two intersected segments
∴ There is a pair of vertically opposite angles
∵ The other isosceles Δ has a vertex angle of measure x
∵ A base angle of the 1st Δ and a base angle of the 2nd Δ are vertically
opposite angles
∴ They are equal in measure
∴ The measure of the base angle of the 2nd Δ = 56°
∴ The two base angles are equal in measure
∴ The measure of each base angle is 56°
→ The sum of the measures of the interior angles of a triangle is 180°
∵ 56° + 56° + x = 180°
∴ 112° + x = 180°
→ Subtract 112 from both sides
∴ x = 68
∴ The measure of angle x is 68°
