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Llana [10]
3 years ago
8

Two angles of a quadrilateral measure 253° and 74°. The other two angles are in a ratio of 5:6. What are the measures of those t

wo angles?
Mathematics
2 answers:
Morgarella [4.7K]3 years ago
7 0

Step-by-step explanation:

<em>Given </em>

<em>1st </em><em>angle </em><em>=</em><em> </em><em>2</em><em>5</em><em>3</em><em>°</em><em> </em><em>2nd </em><em>angle </em><em>=</em><em> </em><em>7</em><em>4</em><em>°</em>

<em>Let </em><em>the </em><em>other </em><em>two </em><em>angels </em><em>be </em><em>5x </em><em>and </em><em>6x. </em>

<em>2</em><em>5</em><em>3</em><em>°</em><em> </em><em>+</em><em> </em><em>7</em><em>4</em><em>°</em><em> </em><em>+</em><em> </em><em>5x </em><em>+</em><em> </em><em>6x </em><em>=</em><em> </em><em>3</em><em>6</em><em>0</em><em>°</em><em> </em><em><</em><em>being </em><em>sum </em><em>of </em><em>angles </em><em>of </em><em>quadrilateral </em><em>></em>

<em>3</em><em>2</em><em>7</em><em>°</em><em> </em><em>+</em><em> </em><em>11x </em><em>=</em><em> </em><em>3</em><em>6</em><em>0</em><em>°</em>

<em>11x </em><em>=</em><em> </em><em>3</em><em>6</em><em>0</em><em>°</em><em> </em><em>-</em><em> </em><em>3</em><em>2</em><em>7</em><em>°</em>

<em>11x </em><em>=</em><em> </em><em>3</em><em>3</em><em>°</em>

<em>Therefore </em><em>x </em><em>=</em><em> </em><em>3</em><em>°</em>

<em>Now</em>

<em>Measures </em><em>of </em><em>two </em><em>angles </em>

<em>5x </em><em>=</em><em> </em><em>5</em><em>*</em><em>3</em><em> </em><em>°</em><em> </em><em>=</em><em> </em><em>1</em><em>5</em><em> </em><em>°</em>

<em>6x </em><em>=</em><em> </em><em>6</em><em> </em><em>*</em><em> </em><em>3</em><em> </em><em>=</em><em> </em><em>1</em><em>8</em><em> </em><em>°</em>

Llana [10]3 years ago
6 0

Answer:

15 and 18 degrees.

Step-by-step explanation:

The total measure of the 2 angles =   327 degrees.

As there are 2 angles and 360 degrees in a  quadrilateral  the other 2 angles

add up to 360 - 27 = 33 degrees.

If they are in the ratio 5:6 their measure is:

33 * 5/(5 + 6) = 33 * 5/11  =  3*5 =<u> </u><u>15 degrees</u> and

33 * 6/11 = 3*6 = <u>18 degrees.</u>

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