Question

what is the value of v?
y
64°
w
58°
x
v =
□°

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\).

Step2: Calculate the third angle

Let the angles be \(64^\circ\), \(58^\circ\), and \(v\). So, \(v = 180 - 64 - 58\).
Calculate \(180 - 64 = 116\), then \(116 - 58 = 58\). Wait, no, wait—wait, the triangle has two equal sides (marked with ticks), so it's isosceles? Wait, no, the ticks are on two sides, so the angles opposite those sides are equal? Wait, no, in the triangle, sides \(YW\) and \(YX\)? Wait, no, the ticks: one on \(YW\) and one on \(YX\)? Wait, no, looking at the triangle, vertices \(Y\), \(W\), \(X\). The sides \(YX\) and \(YW\) have ticks? Wait, no, the ticks are on \(YW\) and \(YX\)? Wait, no, the angle at \(Y\) is \(64^\circ\), at \(W\) is \(58^\circ\), and at \(X\) is \(v\). Wait, maybe I made a mistake. Wait, the sum of angles in a triangle is \(180^\circ\), so \(v = 180 - 64 - 58\). Wait, \(64 + 58 = 122\), so \(180 - 122 = 58\)? No, that can't be. Wait, no, maybe the triangle is isosceles, so the sides with ticks are equal, so the angles opposite are equal. Wait, the side between \(Y\) and \(W\) and the side between \(Y\) and \(X\) have ticks? So those two sides are equal, so the angles opposite them: angle at \(X\) (opposite \(YW\)) and angle at \(W\) (opposite \(YX\))? Wait, no, let's label the triangle: \(Y\) is a vertex, \(W\) and \(X\) are the other two. The side \(YW\) and \(YX\) have ticks, so \(YW = YX\), so the angles opposite: angle at \(X\) (opposite \(YW\)) and angle at \(W\) (opposite \(YX\)) are equal? Wait, angle at \(X\) is \(v\), angle at \(W\) is \(58^\circ\). So if \(YW = YX\), then angle at \(X\) = angle at \(W\)? But angle at \(W\) is \(58^\circ\), so \(v = 58^\circ\)? But then angle at \(Y\) is \(64^\circ\), sum would be \(58 + 58 + 64 = 180\)? \(58 + 58 = 116\), \(116 + 64 = 180\). Yes! So that's correct. So \(v = 58^\circ\)? Wait, no, wait, angle at \(Y\) is \(64^\circ\), angles at \(X\) and \(W\) are equal? Wait, no, the sides \(YW\) and \(YX\) are equal, so the angles opposite them: angle at \(X\) (opposite \(YW\)) and angle at \(W\) (opposite \(YX\)) are equal. So angle at \(X\) (v) = angle at \(W\) (58°)? But then sum is \(64 + 58 + 58 = 180\), which works. So \(v = 58^\circ\)? Wait, but earlier calculation without considering isosceles: \(180 - 64 - 58 = 58\), which matches. So that's correct.

Wait, no, wait, let's do it again. Sum of angles in a triangle: \( \angle Y + \angle W + \angle X = 180^\circ \). \( \angle Y = 64^\circ \), \( \angle W = 58^\circ \), so \( \angle X = 180 - 64 - 58 = 58^\circ \). So \( v = 58^\circ \).

Answer:

\( 58 \)