How to find an angle in other quadrilaterals - ISEE Upper Level Quantitative Reasoning

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Question

Three of the interior angles of a quadrilateral measure $51^{\circ }$ , $120 ^{\circ }$ , and $77^{\circ}$ . What is the measure of the fourth interior angle?

Answer

The measures of the angles of a quadrilateral have sum $360^{\circ }$ . If is the measure of the unknown angle, then:

The angle measures $112^{\circ }$ .

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Question

The angles of a quadrilateral measure $x^{\circ }, x^{\circ }, \left ( x+45 \right ) ^{\circ }, \left ( x+65 \right ) ^{\circ }$ . Evaluate .

Answer

The sum of the degree measures of the angles of a quadrilateral is 360, so we can set up and solve for in the equation:

$x + x + \left ( x+45 \right ) + \left ( x+65 \right ) = 360$

$4x\div 4 = 250 \div 4$

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Question

The four angles of a quadrilateral have the following value: 79 degrees, 100 degrees, 50 degrees, and degrees. What is the value of ?

Answer

Given that there are 360 degrees when all the angles of a quadrilateral are added toghether, this problem can be solved with the following equation:

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Question

In a quadrilateral, the angles have the following values:

$94^{\circ},27^{\circ},81^{\circ},\textup{and }(4x)^{\circ}$ .

What is the value of ?

Answer

Given that there are 360 degrees when the angles of a quadrilateral are added together, it follows that:

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Question

Three of the interior angles of a quadrilateral measure $51^{\circ }$ , $120 ^{\circ }$ , and $77^{\circ}$ . What is the measure of the fourth interior angle?

Answer

The measures of the angles of a quadrilateral have sum $360^{\circ }$ . If is the measure of the unknown angle, then:

The angle measures $112^{\circ }$ .

Compare your answer with the correct one above

Question

The angles of a quadrilateral measure $x^{\circ }, x^{\circ }, \left ( x+45 \right ) ^{\circ }, \left ( x+65 \right ) ^{\circ }$ . Evaluate .

Answer

The sum of the degree measures of the angles of a quadrilateral is 360, so we can set up and solve for in the equation:

$x + x + \left ( x+45 \right ) + \left ( x+65 \right ) = 360$

$4x\div 4 = 250 \div 4$

Compare your answer with the correct one above

Question

The four angles of a quadrilateral have the following value: 79 degrees, 100 degrees, 50 degrees, and degrees. What is the value of ?

Answer

Given that there are 360 degrees when all the angles of a quadrilateral are added toghether, this problem can be solved with the following equation:

Compare your answer with the correct one above

Question

In a quadrilateral, the angles have the following values:

$94^{\circ},27^{\circ},81^{\circ},\textup{and }(4x)^{\circ}$ .

What is the value of ?

Answer

Given that there are 360 degrees when the angles of a quadrilateral are added together, it follows that:

Compare your answer with the correct one above

Question

Three of the interior angles of a quadrilateral measure $51^{\circ }$ , $120 ^{\circ }$ , and $77^{\circ}$ . What is the measure of the fourth interior angle?

Answer

The measures of the angles of a quadrilateral have sum $360^{\circ }$ . If is the measure of the unknown angle, then:

The angle measures $112^{\circ }$ .

Compare your answer with the correct one above

Question

The angles of a quadrilateral measure $x^{\circ }, x^{\circ }, \left ( x+45 \right ) ^{\circ }, \left ( x+65 \right ) ^{\circ }$ . Evaluate .

Answer

The sum of the degree measures of the angles of a quadrilateral is 360, so we can set up and solve for in the equation:

$x + x + \left ( x+45 \right ) + \left ( x+65 \right ) = 360$

$4x\div 4 = 250 \div 4$

Compare your answer with the correct one above

Question

The four angles of a quadrilateral have the following value: 79 degrees, 100 degrees, 50 degrees, and degrees. What is the value of ?

Answer

Given that there are 360 degrees when all the angles of a quadrilateral are added toghether, this problem can be solved with the following equation:

Compare your answer with the correct one above

Question

In a quadrilateral, the angles have the following values:

$94^{\circ},27^{\circ},81^{\circ},\textup{and }(4x)^{\circ}$ .

What is the value of ?

Answer

Given that there are 360 degrees when the angles of a quadrilateral are added together, it follows that:

Compare your answer with the correct one above

Question

Three of the interior angles of a quadrilateral measure $51^{\circ }$ , $120 ^{\circ }$ , and $77^{\circ}$ . What is the measure of the fourth interior angle?

Answer

The measures of the angles of a quadrilateral have sum $360^{\circ }$ . If is the measure of the unknown angle, then:

The angle measures $112^{\circ }$ .

Compare your answer with the correct one above

Question

The angles of a quadrilateral measure $x^{\circ }, x^{\circ }, \left ( x+45 \right ) ^{\circ }, \left ( x+65 \right ) ^{\circ }$ . Evaluate .

Answer

The sum of the degree measures of the angles of a quadrilateral is 360, so we can set up and solve for in the equation:

$x + x + \left ( x+45 \right ) + \left ( x+65 \right ) = 360$

$4x\div 4 = 250 \div 4$

Compare your answer with the correct one above

Question

The four angles of a quadrilateral have the following value: 79 degrees, 100 degrees, 50 degrees, and degrees. What is the value of ?

Answer

Given that there are 360 degrees when all the angles of a quadrilateral are added toghether, this problem can be solved with the following equation:

Compare your answer with the correct one above

Question

In a quadrilateral, the angles have the following values:

$94^{\circ},27^{\circ},81^{\circ},\textup{and }(4x)^{\circ}$ .

What is the value of ?

Answer

Given that there are 360 degrees when the angles of a quadrilateral are added together, it follows that:

Compare your answer with the correct one above

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