In triangle ABC, the measure of angle A is half the measure of angle B, and the measure of angle C is 50° less than the measure

Question

4 years ago

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In triangle ABC, the measure of angle A is half the measure of angle B, and the measure of angle C is 50° less than the measure

of angle B. Find the measure of the smallest angle. (Recall that the sum of the measures of the angles in a triangle is 180°.)

Mathematics

1 answer:

kow [346] · Answer 1 · 2022-01-04T11:19:26+03:00

Answer:

42º

Step-by-step explanation:

You can start by setting up the equations that are given in the stem of the problem: a=.5b, c=b-50, a+b+c=180. Then plug in the values of b in relation to the other values into the equation a+b+c=180. This will give you (.5b)+b+(b-50)=180. By expanding this and combining like terms, we will get 2.5b=230. By dividing each side by 2.5, we get b=92. Then, referencing the first equations, a=.5(92)=46, and c=92-50=42. The smallest of all of these is c, 42.