156,699 views
25 votes
25 votes
Multiple Choice If m

Multiple Choice If m-example-1
User DotDotDot
by
2.6k points

1 Answer

19 votes
19 votes

SOLUTION

Consider the image given below,

Since the diagonals of a kite are perpendicular, hence the angles at the center are 90 degrees.

Hence

From triangles of the shorter diagonals, triangle, ADC


\angle DAE=\angle DCE\text{ (bases angles of isosceles triangle)}

Then


\begin{gathered} \angle ADE+\angle AED+\angle DAE=180^0(\text{ sum of angles in a triangle)} \\ \text{Where } \\ \angle ADE=48^0,\angle AED=90^0,\angle DAE=\angle DCE^{} \end{gathered}

substituting the values we have


\begin{gathered} 48^0+90^0+\angle DCE=180^0 \\ 138^0+\angle DCE=180^0 \end{gathered}

Then, subtracting 138 from both sides we have


\begin{gathered} \angle DCE=180^0-138^0 \\ \angle DCE=42^0 \end{gathered}

Hence

The measure of angle DCE= 42 degrees

Similarly, considering the triangle CAB


\begin{gathered} \angle BCE=\angle BAE(\text{ base angle of an isosceles triangle )} \\ \text{Where } \\ \angle BCE=67^0 \end{gathered}

Then


\angle BCE+\angle BAE+\angle ABC=180^0(\text{ sum fo angles in a triangle CAB)}

Hence


\begin{gathered} 67^0+67^0+\angle ABC=180^0 \\ 134^0+\angle ABC=180^0 \end{gathered}

Subtracting 134 from both sides, we have


\begin{gathered} \angle ABC=180^0-134^0 \\ \angle ABC=46^0 \end{gathered}

Hence

m < ABC =46°

Answer: m

Multiple Choice If m-example-1
User Scrayne
by
3.8k points