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Question
In triangle ABC, if AB-BC and
∠
B=70°,
∠
A will be:
70°
110°
55°
130°
ANSWER : 3
Descrption
<p style="margin-left:0px;">In triangle ABC, you're given that:</p><ol><li>AB = BC</li><li>∠B = 70°</li></ol><p style="margin-left:0px;">We need to find the measure of ∠A.</p><p style="margin-left:0px;">Since AB = BC, it means that triangle ABC is an isosceles triangle, which means that the two sides AB and BC are equal in length. In an isosceles triangle, the angles opposite these equal sides are also equal.</p><p style="margin-left:0px;">So, in triangle ABC, ∠A = ∠C.</p><p style="margin-left:0px;">Now, since ∠B = 70°, and the sum of angles in a triangle is always 180°, we can find ∠A and ∠C using the following equation:</p><p style="margin-left:0px;">∠A + ∠B + ∠C = 180°</p><p style="margin-left:0px;">Plugging in the values:</p><p style="margin-left:0px;">∠A + 70° + ∠C = 180°</p><p style="margin-left:0px;">Now, substitute ∠A = ∠C:</p><p style="margin-left:0px;">∠A + 70° + ∠A = 180°</p><p style="margin-left:0px;">Combine like terms:</p><p style="margin-left:0px;">2∠A + 70° = 180°</p><p style="margin-left:0px;">Subtract 70° from both sides:</p><p style="margin-left:0px;">2∠A = 180° - 70° 2∠A = 110°</p><p style="margin-left:0px;">Now, divide by 2:</p><p style="margin-left:0px;">∠A = 110° / 2 ∠A = 55°</p><p style="margin-left:0px;">So, ∠A is 55°.</p>
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