Question

ASAP Please

Three of the angles in a quadrilateral are 100°, 65° and 100°.
a. Show how you can calculate the fourth angle.
b. Suggest which type of quadrilateral this shape may be.

Answer 1

a. 95 b. kite

Explanation:

a. all quadrilaterals add up to 360° angle with all angles, so 100+100+65=265, 360-265=95.

b. most quadrilaterals have 2 pairs of 2 equilateral angles, and this is one of the only ones that doesnt.

Answer 2

a) 95°

b) Kite

Explanation:

Part (a)

Theorem: Interior angles of a quadrilateral sum to 360°.

Given angles:

• 100°
• 65°
• 100°

Let x be the unknown angle.

⇒ 100° + 65° + 100° + x = 360°

⇒ 265° + x = 360°

⇒ 265° + x - 265° = 360° - 265°

⇒ x = 95°

Therefore, the fourth angle is 95°.

Part (b)

A kite is a quadrilateral that has one pair of congruent opposite angles.

Therefore, as two of the interior angles of the given quadrilateral are equal, the shape may be a kite.