# Answer to Question #23507 in Analytic Geometry for arjay abainza

Question #23507
one acute angle of a right triangle measures 10 degrees more than 3 times the measures of the other acute angle. what are the measures of the three angle
1
2013-02-04T09:14:51-0500
Let&#039;s denote the measures of the angles of the triangle by A, B and C. As the triangle is right, the measure of the third angle is C = 90&deg;. The sum of the measures of the other two angles need to be

A + B = 180 - C = 180&deg; - 90&deg; = 90&deg;, (1)

as the sum of all the angles of an arbitrary triangle is 180&deg;. Also we know that

A - 10&deg; = 3B (2).

So, we&#039;ve got the system of equations (1), (2). Let&#039;s solve it:

(2) ==&gt; A = 3B + 10&deg;;

(1): A + B = 90&deg; ==&gt; 3B + 10&deg; + B = 90&deg; ==&gt; 4B = 80&deg; ==&gt; B = 20&deg;;

A = 3B + 10&deg; = 3*20&deg; + 10&deg; = 70&deg;.

So, the measures of the angles of the triangle are 20&deg;, 70&deg; and 90&deg;.

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