In an isoseles triangle where <W a d <X are congruent. If m<W is 56°, what is m<Z?
In an isosceles triangle, the base angles (the angles opposite the congruent sides) are congruent. So if we let the measure of angle W be 56°, then the measure of angle X is also 56°.
In an isosceles triangle, the sum of the angles is always 180°. So the measure of angle W + angle X + angle Z = 180°.
Substituting the given measures, we have:
56° + 56° + m<Z = 180°
Simplifying, we get:
112° + m<Z = 180°
Next, let's isolate the variable by subtracting 112° from both sides of the equation:
m<Z = 180° - 112°
m<Z = 68°
Therefore, the measure of angle Z is 68°.
To find the measure of angle Z in an isosceles triangle, you need to know the measure of one of the congruent angles. In this case, you know that angle W is congruent to angle X.
Given that angle W is 56°, and angle W is congruent to angle X, you can conclude that angle X is also 56°.
Since angle W and angle X are the base angles of an isosceles triangle, angle Z must be the vertex angle. In an isosceles triangle, the vertex angle is always equal to the sum of the two base angles.
So, to find the measure of angle Z, you need to calculate the sum of angle W and angle X:
m<Z = m<W + m<X = 56° + 56° = 112°
Therefore, the measure of angle Z is 112°.
To find the measure of angle Z in the isosceles triangle, we need to use the fact that the sum of the angles in a triangle is always 180 degrees.
Since angle W and angle X are congruent in an isosceles triangle, we can denote the measure of angle X as m<X.
Given that the measure of angle W is 56 degrees, we can set up the equation:
m<W + m<X + m<Z = 180
Substituting the given values:
56 + m<X + m<Z = 180
To solve for m<Z, we need to isolate it on one side of the equation:
m<Z = 180 - 56 - m<X
Since m<X and m<Z are congruent angles in an isosceles triangle, we can simplify the equation to:
m<Z = 180 - 56 - m<Z
Combining like terms:
2m<Z = 180 - 56
Evaluating the equation:
2m<Z = 124
Finally, to find the measure of angle Z, we divide both sides of the equation by 2:
m<Z = 124/2
m<Z = 62
Therefore, the measure of angle Z is 62 degrees.