Question

what are the values of u and v?
a
40°
u
b
u =
v =
submit

Explanation:

Step1: Use the property of isosceles triangle

Since two sides of \(\triangle ABC\) are equal (marked with the same tick - marks), \(\triangle ABC\) is isosceles. In an isosceles triangle, the base angles are equal. But here, we know that the sum of angles in a triangle is \(180^{\circ}\). Let \(\angle A = 40^{\circ}\), \(\angle B=u\), \(\angle C = v\).

Step2: Find the value of \(u\)

Since the triangle has two equal sides, and the sum of angles in a triangle \(\angle A+\angle B+\angle C=180^{\circ}\). Also, from the side - mark equality, we know that \(\angle B\) is the largest angle (opposite the longer side in a non - equilateral isosceles triangle is not the case here, wait, no, actually, if two sides are equal, then the angles opposite them are equal. Wait, no, looking at the side - marks: two sides are equal. So \(\angle B\) is the angle opposite the unequal side? No, no, wait, the two sides with tick - marks are equal. So \(\angle A = 40^{\circ}\), and the sum of angles in a triangle: \(u + v+40^{\circ}=180^{\circ}\). Also, since two sides are equal (the sides adjacent to \(\angle A\) and \(\angle C\) are not, wait no, the two sides: if we assume the two sides (not adjacent to \(\angle A\)) are equal. Wait, no, in a triangle, if two sides are equal, then the angles opposite them are equal. Wait, no, looking at the side - marks: two sides (the sides \(AB\) and \(BC\)) are equal. So \(\angle A=\angle C\). But no, wait, no, the side - marks: if two sides (say \(AB\) and \(BC\)) are marked equal. Wait, no, looking at standard notation: in \(\triangle ABC\), if \(AB = BC\), then \(\angle A=\angle C\). But no, wait, no, the side - marks: if two sides (the sides \(AC\) and \(BC\)) are not. Wait, no, looking at the problem again: the two sides (the sides that are not \(\angle A\)'s sides) are marked equal. Wait, no, in a triangle, the sum of angles is \(180^{\circ}\). Let's use the property: if two sides are equal (the sides \(AB\) and \(BC\) are marked equal. Wait, no, the side - marks: assume \(AB = BC\). Then \(\angle A=\angle C\). But \(\angle A = 40^{\circ}\), so \(v = 40^{\circ}\). Then \(u=180^{\circ}-40^{\circ}-40^{\circ}=100^{\circ}\). Wait, no, wait, no, hold on. Wait, in a triangle, if two sides are equal (the sides \(AB\) and \(AC\) are marked equal? No, the side - marks: two sides (the sides \(AB\) and \(BC\)) are marked equal. No, no, wait, the side - marks: in the figure, two sides (the sides that are not \(\angle A\)'s adjacent sides) are marked equal. Wait, no, the sum of angles in a triangle: \(\angle A+\angle B+\angle C = 180^{\circ}\). If two sides are equal (the sides \(AB\) and \(BC\) are marked equal. Then \(\angle A=\angle C\). But \(\angle A = 40^{\circ}\), so \(v = 40^{\circ}\), and \(u=180 - 40-40=100^{\circ}\).

Answer:

\(u = 100^{\circ}\), \(v = 40^{\circ}\)