Question

Atics Geometry

Find missing angles in triangles using ratios 47U
A triangle has an angle that measures 85°. The other two angles are in a ratio of 6:13. What
are the measures of those two angles?
and

Answer 1

The two angles in the triangle are 30° and 65°.

Step-by-step explanation:

Let the two angles in the ratio be 6x and 13x. The sum of the three angles in a triangle is always 180°. Therefore, we can set up the equation: 85 + 6x + 13x = 180.

Simplifying the equation, we get 19x + 85 = 180.

Subtracting 85 from both sides, we have 19x = 95.

Dividing both sides by 19, we find that x = 5.

Therefore, the two angles are 6x = 6(5) = 30° and 13x = 13(5) = 65°.

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