Answer:
1. 55°
2. 82°
3. 11cm
4. 99°
Step-by-step explanation:
1. In a parallelogram, opposite angles are equal; therefore, m∠L = m∠J = 55°
2. In a parallelogram, consecutive angles are supplementary; therefore,
m∠J = 180 - m∠K = 180 - 98 = 82°
3. In a rectangle, opposite sides are equal; therefore, EF = HG
[tex]2x+3=3x-1[/tex]
[tex]3x-2x=3+1[/tex]
[tex]x=4[/tex]
[tex]EF=2x+3=2(4)+3=11cm[/tex]
For checking, compute the length of HG
[tex]HG=3x-1=3(4)-1=11cm[/tex]
4. The sum of the interior angles of quadrilateral (including rhombus) is 360°. Since the sum of the three angles are given, the measurement of one angle can be computed.
∠x = 360 - 279 = 81°
Is this the measure of ∠V? Based on the figure, ∠V is an obtuse angle; hence, ∠V can be known may determining the supplement of 81°.
∠V = 180 - 81 = 99°
