In a parallelogram ABCD find the measure of all the angles if one its angles is 15° less than twice the smallest angle.
Answers
Answer:
In a parallelogram ABCD,
Let ∠A be x. Then, ∠B will be 2x−
15°
We know that, in a parallelogram sum of adjacent angles are supplementary.
∴ ∠A+∠B=180° \\ \\ ⇒ x+2x−15°=180°
⇒ 3x=195°
⇒ x=65°.
∴ ∠A=65°
⇒ ∠B=2x−15°=2×65°−15°=115°.
We know that, in parallelogram opposite angles are equal.
∴ ∠A=∠C and ∠B=∠D
∴ ∠C=65°and ∠D=115°.
∴ The measure of all angles of a parallelogram are 65°,115°,65° and 115°.
Step-by-step explanation:
I hope its helps you
Answer:
65°, 115°, 65°, 115°
Step-by-step explanation:
In parallelogram ABCD,
Let A be x. Then, ZB will be 2x – 15⁰ -
We know that, in a parallelogram sum of adjacent angles are supplementary.
:. A+B = 180°
⇒ x + 2x - 15⁰: = 180°
⇒ 3x = 195⁰
⇒ x = 65°.
:. A = 65°
⇒ B= 2- 15° = 2 × 65° - 15º = 115⁰.
We know that, in parallelogram opposite angles are equal.
:. A= C and B = D
:. C= 65° and D= 115°
:. The measure of all angles of a parallelogram are 65°, 115°, 65° and 115°.
Note:
Before the vertex' (A, B, C, D) please mark a sign of angle.