Question

find the angle measures given the figure is a rhombus.​

Answer 1

$\large \tt{{❃ \: S \: O \: L \: U \: T \: I \: O \: N : }}$

• A rhombus is a parallelogram in which all sides are equal i.e AB = BC = CD = CA

• Let ∠ A be x. In the ∆ ABC , AB = AC which means they are isosceles triangle and we know the opposite angles of isosceles triangle are equal i.e ∠ A = ∠ C = x.

• The sum of angles of a triangle is always 180°. Now , Find out the value of x :

$\large{ \tt{❁ \:x + x + 98 = 180 \degree \: [ Sum\: of \: angle \: of \: a \: triangle ]}}$

$\large{ \tt{⟶2x + 98 \degree= 180 \degree}}$

$\large{ \tt{⟶ \: 2x = 180 \degree - 98 \degree}}$

$\large{ \tt{⟶ \: 2x = 82 \degree}}$

$\large{ \tt{ ⟶x = \frac{82 \degree}{2} }}$

$\large{ \tt{⟶ \: x = 41 \degree}}$

• The value of x is 41°. Now , Find the measure of ∠ 1 :

$\large{ \tt{ ↔\angle \: 1 = x \degree = \boxed{41 \degree}}}$ [ Being alternate angles ]

• Hence , Our final answer is 41° .

- Alternate angles are the non-adjacent interiors pair of angles lying to the opposite side of a transversal when it intersects two straight line segments. Alternate angles form ' Z ' shape.

• Hope I helped! Let me know if you have any questions regarding my answer. :)